module string | startPos dict | endPos dict | nextStartPos dict | goals list | goalsAfter list | ppTac string | elaborator string | kind string |
|---|---|---|---|---|---|---|---|---|
Mathlib.Tactic.ComputeAsymptotics.Lemmas | {
"line": 56,
"column": 2
} | {
"line": 56,
"column": 44
} | {
"line": 57,
"column": 4
} | [
{
"pp": "α : Type u_1\n𝕜 : Type u_2\ninst✝⁴ : Field 𝕜\ninst✝³ : LinearOrder 𝕜\ninst✝² : IsStrictOrderedRing 𝕜\ninst✝¹ : TopologicalSpace 𝕜\ninst✝ : OrderTopology 𝕜\nl : Filter α\nf : 𝕜 → α\nc : 𝕜\nh_neg : Tendsto (fun x ↦ f (c - x⁻¹)) atTop l\nh_pos : Tendsto (fun x ↦ f (c + x⁻¹)) atTop l\n⊢ Tendsto f (... | [
"α : Type u_1\n𝕜 : Type u_2\ninst✝⁴ : Field 𝕜\ninst✝³ : LinearOrder 𝕜\ninst✝² : IsStrictOrderedRing 𝕜\ninst✝¹ : TopologicalSpace 𝕜\ninst✝ : OrderTopology 𝕜\nl : Filter α\nf : 𝕜 → α\nc : 𝕜\nh_neg : Tendsto (fun x ↦ f (c - x⁻¹)) atTop l\nh_pos : Tendsto (fun x ↦ f (c + x⁻¹)) atTop l\n⊢ map f (𝓝[<] c) ≤ l ∧ m... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.SetTheory.Ordinal.Notation | {
"line": 841,
"column": 25
} | {
"line": 841,
"column": 51
} | {
"line": 841,
"column": 52
} | [
{
"pp": "a0 a' : ONote\nN0 : a0.NF\nNa' : a'.NF\nm : ℕ\nd : ω ∣ a'.repr\ne0 : a0.repr ≠ 0\nh : a'.repr + ↑m < ω ^ a0.repr\nn : ℕ+\nNo : (a0.oadd n a').NF\nk : ℕ\nR' : Ordinal.{0} := (opowAux 0 a0 (a0.oadd n a' * ↑m) (k + 1) m).repr\nR : Ordinal.{0} := (opowAux 0 a0 (a0.oadd n a' * ↑m) k m).repr\nω0 : Ordinal.{0... | [
"a0 a' : ONote\nN0 : a0.NF\nNa' : a'.NF\nm : ℕ\nd : ω ∣ a'.repr\ne0 : a0.repr ≠ 0\nh : a'.repr + ↑m < ω ^ a0.repr\nn : ℕ+\nNo : (a0.oadd n a').NF\nk : ℕ\nR' : Ordinal.{0} := (opowAux 0 a0 (a0.oadd n a' * ↑m) (k + 1) m).repr\nR : Ordinal.{0} := (opowAux 0 a0 (a0.oadd n a' * ↑m) k m).repr\nω0 : Ordinal.{0} := ω ^ a0.... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Tactic.ComputeAsymptotics.Multiseries.Majorized | {
"line": 68,
"column": 2
} | {
"line": 68,
"column": 42
} | {
"line": 70,
"column": 0
} | [
{
"pp": "f b : ℝ → ℝ\nexp1 exp2 : ℝ\nh_lt : exp1 ≤ exp2\nh : ∀ exp' > exp1, f =o[atTop] (b ^ exp')\n⊢ ∀ exp' > exp2, f =o[atTop] (b ^ exp')",
"ppTerm": "?m.5",
"assigned": true,
"usedConstants": [
"Real.instIsOrderedRing",
"Mathlib.Tactic.Ring.Common.neg_zero",
"Eq.mpr",
"Neg... | [] | exact fun exp' h_exp ↦ h _ (by linarith) | Lean.Elab.Tactic.evalExact | Lean.Parser.Tactic.exact |
Mathlib.Tactic.ComputeAsymptotics.Multiseries.Majorized | {
"line": 73,
"column": 2
} | {
"line": 73,
"column": 37
} | {
"line": 73,
"column": 38
} | [
{
"pp": "f b : ℝ → ℝ\nexp : ℝ\nh_lt : exp < 0\nh : Majorized f b exp\n⊢ Tendsto f atTop (𝓝 0)",
"ppTerm": "?m.13",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"f b : ℝ → ℝ\nexp : ℝ\nh_lt : exp < 0\nh : Majorized f b exp\n⊢ Tendsto f atTop (𝓝 0)"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.SetTheory.Ordinal.Notation | {
"line": 849,
"column": 8
} | {
"line": 849,
"column": 29
} | {
"line": 849,
"column": 30
} | [
{
"pp": "case pos.succ\na0 a' : ONote\nN0 : a0.NF\nNa' : a'.NF\nd : ω ∣ a'.repr\ne0 : a0.repr ≠ 0\nn : ℕ+\nNo : (a0.oadd n a').NF\nk : ℕ\nω0 : Ordinal.{0} := ω ^ a0.repr\nα' : Ordinal.{0} := ω0 * ↑↑n + a'.repr\nα0 : 0 < α'\nω00 : 0 < ω0 ^ ↑k\nk0 : k = 0\nm : ℕ\nh : a'.repr + ↑(m + 1) < ω ^ a0.repr\nR' : Ordinal... | [
"case pos.succ\na0 a' : ONote\nN0 : a0.NF\nNa' : a'.NF\nd : ω ∣ a'.repr\ne0 : a0.repr ≠ 0\nn : ℕ+\nNo : (a0.oadd n a').NF\nk : ℕ\nω0 : Ordinal.{0} := ω ^ a0.repr\nα' : Ordinal.{0} := ω0 * ↑↑n + a'.repr\nα0 : 0 < α'\nω00 : 0 < ω0 ^ ↑k\nk0 : k = 0\nm : ℕ\nh : a'.repr + ↑(m + 1) < ω ^ a0.repr\nR' : Ordinal.{0} := (opo... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Tactic.ComputeAsymptotics.Multiseries.Basis | {
"line": 94,
"column": 4
} | {
"line": 94,
"column": 55
} | {
"line": 94,
"column": 56
} | [
{
"pp": "case left\nleft right : Basis\nh_left : List.Pairwise (fun x y ↦ (Real.log ∘ y) =o[atTop] (Real.log ∘ x)) left ∧ ∀ f ∈ left, Tendsto f atTop atTop\nh_right : List.Pairwise (fun x y ↦ (Real.log ∘ y) =o[atTop] (Real.log ∘ x)) right ∧ ∀ f ∈ right, Tendsto f atTop atTop\nh : ∀ f ∈ left, ∀ g ∈ right, (Real.... | [
"case left\nleft right : Basis\nh_left : List.Pairwise (fun x y ↦ (Real.log ∘ y) =o[atTop] (Real.log ∘ x)) left ∧ ∀ f ∈ left, Tendsto f atTop atTop\nh_right : List.Pairwise (fun x y ↦ (Real.log ∘ y) =o[atTop] (Real.log ∘ x)) right ∧ ∀ f ∈ right, Tendsto f atTop atTop\nh : ∀ f ∈ left, ∀ g ∈ right, (Real.log ∘ g) =o[... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Tactic.ComputeAsymptotics.Multiseries.Basis | {
"line": 102,
"column": 2
} | {
"line": 102,
"column": 62
} | {
"line": 104,
"column": 0
} | [
{
"pp": "basis : Basis\nf : ℝ → ℝ\nh_basis : WellFormedBasis basis\nhf_tendsto : Tendsto f atTop atTop\nhf : ∀ g ∈ basis, (Real.log ∘ g) =o[atTop] (Real.log ∘ f)\n⊢ WellFormedBasis ([f] ++ basis)",
"ppTerm": "?m.33",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"False",
"Real",
... | [] | exact append (by simpa [WellFormedBasis]) h_basis (by simpa) | Lean.Elab.Tactic.evalExact | Lean.Parser.Tactic.exact |
Mathlib.SetTheory.Ordinal.Notation | {
"line": 862,
"column": 8
} | {
"line": 862,
"column": 19
} | {
"line": 862,
"column": 20
} | [
{
"pp": "case hbc.refine_1\na0 a' : ONote\nN0 : a0.NF\nNa' : a'.NF\nm : ℕ\nd : ω ∣ a'.repr\ne0✝ : a0.repr ≠ 0\nh : a'.repr + ↑m < ω ^ a0.repr\nn : ℕ+\nNo : (a0.oadd n a').NF\nk : ℕ\nR' : Ordinal.{0} := (opowAux 0 a0 (a0.oadd n a' * ↑m) (k + 1) m).repr\nR : Ordinal.{0} := (opowAux 0 a0 (a0.oadd n a' * ↑m) k m).r... | [
"case hbc.refine_1\na0 a' : ONote\nN0 : a0.NF\nNa' : a'.NF\nm : ℕ\nd : ω ∣ a'.repr\ne0✝ : a0.repr ≠ 0\nh : a'.repr + ↑m < ω ^ a0.repr\nn : ℕ+\nNo : (a0.oadd n a').NF\nk : ℕ\nR' : Ordinal.{0} := (opowAux 0 a0 (a0.oadd n a' * ↑m) (k + 1) m).repr\nR : Ordinal.{0} := (opowAux 0 a0 (a0.oadd n a' * ↑m) k m).repr\nω0 : Or... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Tactic.ComputeAsymptotics.Multiseries.Basis | {
"line": 155,
"column": 4
} | {
"line": 155,
"column": 53
} | {
"line": 155,
"column": 54
} | [
{
"pp": "case hf_comp\nbasis_hd : ℝ → ℝ\nbasis_tl : Basis\nh_basis : WellFormedBasis (basis_hd :: basis_tl)\ng : ℝ → ℝ\nhg : (basis_hd :: basis_tl).getLast? = some g\n⊢ (Real.log ∘ Real.log ∘ (basis_hd :: basis_tl).getLast ⋯) =o[atTop] (Real.log ∘ g)",
"ppTerm": "?hf_comp",
"assigned": true,
"usedCo... | [
"case hf_comp\nbasis_hd : ℝ → ℝ\nbasis_tl : Basis\nh_basis : WellFormedBasis (basis_hd :: basis_tl)\ng : ℝ → ℝ\nhg : (basis_hd :: basis_tl).getLast? = some g\n⊢ (Real.log ∘ Real.log ∘ g) =o[atTop] (Real.log ∘ g)"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Tactic.ComputeAsymptotics.Multiseries.Basic | {
"line": 161,
"column": 4
} | {
"line": 161,
"column": 59
} | {
"line": 161,
"column": 60
} | [
{
"pp": "case cons\nc : ℝ\nbasis_hd : ℝ → ℝ\nbasis_tl : List (ℝ → ℝ)\n⊢ (const (basis_hd :: basis_tl) c).Sorted",
"ppTerm": "?cons",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Real",
"congrArg",
"Tactic.ComputeAsymptotics.MultiseriesExpansion.Sorted",
"id",
"... | [
"case cons\nc : ℝ\nbasis_hd : ℝ → ℝ\nbasis_tl : List (ℝ → ℝ)\n⊢ (Multiseries.const basis_hd basis_tl c).Sorted"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Tactic.ComputeAsymptotics.Multiseries.Basis | {
"line": 216,
"column": 20
} | {
"line": 216,
"column": 42
} | {
"line": 216,
"column": 43
} | [
{
"pp": "case keep\nbasis : Basis\nbasis_hd✝ : ℝ → ℝ\nbasis_tl✝ : Basis\nex : BasisExtension basis_tl✝\nih : List.Sublist basis_tl✝ ex.getBasis\n⊢ (basis_hd✝ :: basis_tl✝).Sublist (keep basis_hd✝ ex).getBasis",
"ppTerm": "?keep",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"List.cons_... | [
"case keep\nbasis : Basis\nbasis_hd✝ : ℝ → ℝ\nbasis_tl✝ : Basis\nex : BasisExtension basis_tl✝\nih : List.Sublist basis_tl✝ ex.getBasis\n⊢ List.Sublist basis_tl✝ ex.getBasis"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.SetTheory.Ordinal.Notation | {
"line": 876,
"column": 39
} | {
"line": 876,
"column": 50
} | {
"line": 876,
"column": 51
} | [
{
"pp": "a0 a' : ONote\nN0 : a0.NF\nNa' : a'.NF\nm : ℕ\nd : ω ∣ a'.repr\ne0 : a0.repr ≠ 0\nh : a'.repr + ↑m < ω ^ a0.repr\nn : ℕ+\nNo : (a0.oadd n a').NF\nk : ℕ\nR' : Ordinal.{0} := (opowAux 0 a0 (a0.oadd n a' * ↑m) (k + 1) m).repr\nR : Ordinal.{0} := (opowAux 0 a0 (a0.oadd n a' * ↑m) k m).repr\nω0 : Ordinal.{0... | [
"a0 a' : ONote\nN0 : a0.NF\nNa' : a'.NF\nm : ℕ\nd : ω ∣ a'.repr\ne0 : a0.repr ≠ 0\nh : a'.repr + ↑m < ω ^ a0.repr\nn : ℕ+\nNo : (a0.oadd n a').NF\nk : ℕ\nR' : Ordinal.{0} := (opowAux 0 a0 (a0.oadd n a' * ↑m) (k + 1) m).repr\nR : Ordinal.{0} := (opowAux 0 a0 (a0.oadd n a' * ↑m) k m).repr\nω0 : Ordinal.{0} := ω ^ a0.... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Tactic.ComputeAsymptotics.Multiseries.Basic | {
"line": 231,
"column": 4
} | {
"line": 231,
"column": 62
} | {
"line": 231,
"column": 63
} | [
{
"pp": "case cons\nn : ℕ\nr : ℝ\nbasis_hd : ℝ → ℝ\nbasis_tl : List (ℝ → ℝ)\n⊢ (monomialRpow (basis_hd :: basis_tl) n r).Sorted",
"ppTerm": "?cons",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Real",
"congrArg",
"Tactic.ComputeAsymptotics.MultiseriesExpansion.monomialRpow... | [
"case cons\nn : ℕ\nr : ℝ\nbasis_hd : ℝ → ℝ\nbasis_tl : List (ℝ → ℝ)\n⊢ (Multiseries.monomialRpow basis_hd basis_tl n r).Sorted"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Tactic.ComputeAsymptotics.Multiseries.Monomial.Basic | {
"line": 147,
"column": 6
} | {
"line": 147,
"column": 36
} | {
"line": 149,
"column": 0
} | [
{
"pp": "case cons.cons\nexp : ℝ\nexps : List ℝ\nih✝ :\n ∀ {basis : Basis},\n WellFormedBasis basis →\n (fun a ↦ (List.zipWith (fun exp b ↦ b a ^ exp) (List.map (fun x ↦ -x) exps) basis).prod) =ᶠ[atTop] fun a ↦\n (List.zipWith (fun exp b ↦ b a ^ exp) exps basis).prod⁻¹\nbasis_hd : ℝ → ℝ\nbasis_t... | [] | grind [Real.rpow_neg h_pos.le] | Lean.Elab.Tactic.evalGrind | Lean.Parser.Tactic.grind |
Mathlib.SetTheory.Ordinal.Notation | {
"line": 898,
"column": 6
} | {
"line": 898,
"column": 24
} | {
"line": 898,
"column": 25
} | [
{
"pp": "case h₂\na0 a' : ONote\nN0 : a0.NF\nNa' : a'.NF\nd : ω ∣ a'.repr\ne0 : a0.repr ≠ 0\nn : ℕ+\nNo : (a0.oadd n a').NF\nk : ℕ\nω0 : Ordinal.{0} := ⋯\nα' : Ordinal.{0} := ⋯\nα0 : 0 < α'\nω00 : 0 < ω0 ^ ↑k\nn✝ : ℕ\nh : a'.repr + ↑(n✝ + 1) < ω ^ a0.repr\nR' : Ordinal.{0} := ⋯\nR : Ordinal.{0} := ⋯\nIH : (k ≠ ... | [
"case h₂\na0 a' : ONote\nN0 : a0.NF\nNa' : a'.NF\nd : ω ∣ a'.repr\ne0 : a0.repr ≠ 0\nn : ℕ+\nNo : (a0.oadd n a').NF\nk : ℕ\nω0 : Ordinal.{0} := ⋯\nα' : Ordinal.{0} := ⋯\nα0 : 0 < α'\nω00 : 0 < ω0 ^ ↑k\nn✝ : ℕ\nh : a'.repr + ↑(n✝ + 1) < ω ^ a0.repr\nR' : Ordinal.{0} := ⋯\nR : Ordinal.{0} := ⋯\nIH : (k ≠ 0 → R < ω0 ^... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.SetTheory.Ordinal.Notation | {
"line": 947,
"column": 4
} | {
"line": 947,
"column": 19
} | {
"line": 948,
"column": 4
} | [
{
"pp": "case oadd\no₁ o₂ : ONote\ninst✝¹ : o₁.NF\ninst✝ : o₂.NF\nm : ℕ\na0 : ONote\nn : ℕ+\na' : ONote\ne₁ : o₁.split = (a0.oadd n a', m)\nN₁ : (a0.oadd n a').NF\nr₁ : o₁.repr = (a0.oadd n a').repr + ↑m\n⊢ (o₁ ^ o₂).repr = o₁.repr ^ o₂.repr",
"ppTerm": "?oadd",
"assigned": true,
"usedConstants": [
... | [
"case oadd\no₁ o₂ : ONote\ninst✝¹ : o₁.NF\ninst✝ : o₂.NF\nm : ℕ\na0 : ONote\nn : ℕ+\na' : ONote\ne₁ : o₁.split = (a0.oadd n a', m)\nN₁ : (a0.oadd n a').NF\nr₁ : o₁.repr = (a0.oadd n a').repr + ↑m\nthis : a0.NF\n⊢ (o₁ ^ o₂).repr = o₁.repr ^ o₂.repr"
] | haveI := N₁.fst | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_tacticHaveI___1 | Lean.Parser.Tactic.tacticHaveI__ |
Mathlib.Tactic.ComputeAsymptotics.Multiseries.Corecursion | {
"line": 224,
"column": 2
} | {
"line": 224,
"column": 13
} | {
"line": 224,
"column": 14
} | [
{
"pp": "α : Type u_1\nop : Stream'.Seq α → Stream'.Seq α\nh : ∀ (x y : Stream'.Seq α), dist (op x) (op y) ≤ ↑1 * dist x y\ns t : Stream'.Seq α\n⊢ dist (op s) (op t) ≤ dist s t",
"ppTerm": "?m.30",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"α : Type u_1\nop : Stream'.Seq α → Stream'.Seq α\nh : ∀ (x y : Stream'.Seq α), dist (op x) (op y) ≤ ↑1 * dist x y\ns t : Stream'.Seq α\n⊢ dist (op s) (op t) ≤ dist s t"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Tactic.ComputeAsymptotics.Multiseries.Defs | {
"line": 222,
"column": 2
} | {
"line": 222,
"column": 24
} | {
"line": 222,
"column": 25
} | [
{
"pp": "basis_hd : ℝ → ℝ\nbasis_tl : Basis\nms : Multiseries basis_hd basis_tl\nh : ms.destruct = none\n⊢ Seq.destruct ms = none",
"ppTerm": "?m.11",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"basis_hd : ℝ → ℝ\nbasis_tl : Basis\nms : Multiseries basis_hd basis_tl\nh : ms.destruct = none\n⊢ Seq.destruct ms = none"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Tactic.ComputeAsymptotics.Multiseries.Corecursion | {
"line": 250,
"column": 4
} | {
"line": 250,
"column": 38
} | {
"line": 251,
"column": 4
} | [
{
"pp": "α : Type u_1\nβ : Type u_2\nγ : Type u_3\nF : β → Option (α × γ × β)\nop : γ → Stream'.Seq α → Stream'.Seq α\nh : FriendlyOperationClass op\nT : (β →ᵤ Stream'.Seq α) → β →ᵤ Stream'.Seq α :=\n fun f b ↦\n match F b with\n | none => nil\n | some (a, c, b') => Seq.cons a (op c (f b'))\n⊢ Lipschi... | [
"α : Type u_1\nβ : Type u_2\nγ : Type u_3\nF : β → Option (α × γ × β)\nop : γ → Stream'.Seq α → Stream'.Seq α\nh : FriendlyOperationClass op\nT : (β →ᵤ Stream'.Seq α) → β →ᵤ Stream'.Seq α :=\n fun f b ↦\n match F b with\n | none => nil\n | some (a, c, b') => Seq.cons a (op c (f b'))\n⊢ ∀ (x y : β →ᵤ Strea... | rw [lipschitzWith_iff_dist_le_mul] | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_rwSeq_1 | Lean.Parser.Tactic.rwSeq |
Mathlib.Tactic.ComputeAsymptotics.Multiseries.Defs | {
"line": 354,
"column": 10
} | {
"line": 354,
"column": 43
} | {
"line": 355,
"column": 2
} | [
{
"pp": "basis_hd : ℝ → ℝ\nbasis_tl : Basis\ns t : Multiseries basis_hd basis_tl\nf g : ℝ → ℝ\nh : mk s f = mk t g\n⊢ s = t ∧ f = g",
"ppTerm": "?m.11",
"assigned": true,
"usedConstants": [
"Stream'.Seq",
"Real",
"congrArg",
"Tactic.ComputeAsymptotics.MultiseriesExpansion.mk.... | [] | by rwa [mk, mk, Prod.mk_inj] at h | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.Tactic.ComputeAsymptotics.Multiseries.Corecursion | {
"line": 266,
"column": 10
} | {
"line": 266,
"column": 21
} | {
"line": 266,
"column": 22
} | [
{
"pp": "α : Type u_1\nβ : Type u_2\nγ : Type u_3\nF : β → Option (α × γ × β)\nop : γ → Stream'.Seq α → Stream'.Seq α\nh : FriendlyOperationClass op\nT : (β →ᵤ Stream'.Seq α) → β →ᵤ Stream'.Seq α :=\n fun f b ↦\n match F b with\n | none => nil\n | some (a, c, b') => Seq.cons a (op c (f b'))\nf g : β →... | [
"α : Type u_1\nβ : Type u_2\nγ : Type u_3\nF : β → Option (α × γ × β)\nop : γ → Stream'.Seq α → Stream'.Seq α\nh : FriendlyOperationClass op\nT : (β →ᵤ Stream'.Seq α) → β →ᵤ Stream'.Seq α :=\n fun f b ↦\n match F b with\n | none => nil\n | some (a, c, b') => Seq.cons a (op c (f b'))\nf g : β →ᵤ Stream'.Se... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Tactic.ComputeAsymptotics.Multiseries.Defs | {
"line": 481,
"column": 6
} | {
"line": 481,
"column": 17
} | {
"line": 481,
"column": 18
} | [
{
"pp": "case seq.h_coef\nbasis_hd : ℝ → ℝ\nbasis_tl : Basis\nms : MultiseriesExpansion (basis_hd :: basis_tl)\nh_coef : ∀ x ∈ ms.seq, x.2.Sorted\nh_Pairwise : Seq.Pairwise (fun x1 x2 ↦ x1 > x2) ms.seq\n⊢ ∀ x ∈ (mk ms.seq 0).seq, x.2.Sorted",
"ppTerm": "?seq.h_coef",
"assigned": true,
"usedConstants... | [
"case seq.h_coef\nbasis_hd : ℝ → ℝ\nbasis_tl : Basis\nms : MultiseriesExpansion (basis_hd :: basis_tl)\nh_coef : ∀ x ∈ ms.seq, x.2.Sorted\nh_Pairwise : Seq.Pairwise (fun x1 x2 ↦ x1 > x2) ms.seq\n⊢ ∀ (a : ℝ) (b : MultiseriesExpansion basis_tl), (a, b) ∈ ms.seq → b.Sorted"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Tactic.ComputeAsymptotics.Multiseries.Defs | {
"line": 482,
"column": 6
} | {
"line": 482,
"column": 17
} | {
"line": 482,
"column": 18
} | [
{
"pp": "case seq.h_Pairwise\nbasis_hd : ℝ → ℝ\nbasis_tl : Basis\nms : MultiseriesExpansion (basis_hd :: basis_tl)\nh_coef : ∀ x ∈ ms.seq, x.2.Sorted\nh_Pairwise : Seq.Pairwise (fun x1 x2 ↦ x1 > x2) ms.seq\n⊢ Seq.Pairwise (fun x1 x2 ↦ x1 > x2) (mk ms.seq 0).seq",
"ppTerm": "?seq.h_Pairwise",
"assigned":... | [
"case seq.h_Pairwise\nbasis_hd : ℝ → ℝ\nbasis_tl : Basis\nms : MultiseriesExpansion (basis_hd :: basis_tl)\nh_coef : ∀ x ∈ ms.seq, x.2.Sorted\nh_Pairwise : Seq.Pairwise (fun x1 x2 ↦ x1 > x2) ms.seq\n⊢ Seq.Pairwise (fun x1 x2 ↦ x2 < x1) ms.seq"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Tactic.ComputeAsymptotics.Multiseries.Defs | {
"line": 486,
"column": 6
} | {
"line": 486,
"column": 17
} | {
"line": 486,
"column": 18
} | [
{
"pp": "case seq.h_coef\nbasis_hd : ℝ → ℝ\nbasis_tl : Basis\nms : MultiseriesExpansion (basis_hd :: basis_tl)\nh_coef : ∀ x ∈ (mk ms.seq 0).seq, x.2.Sorted\nh_Pairwise : Seq.Pairwise (fun x1 x2 ↦ x1 > x2) (mk ms.seq 0).seq\n⊢ ∀ x ∈ ms.seq, x.2.Sorted",
"ppTerm": "?seq.h_coef",
"assigned": true,
"us... | [
"case seq.h_coef\nbasis_hd : ℝ → ℝ\nbasis_tl : Basis\nms : MultiseriesExpansion (basis_hd :: basis_tl)\nh_coef : ∀ x ∈ (mk ms.seq 0).seq, x.2.Sorted\nh_Pairwise : Seq.Pairwise (fun x1 x2 ↦ x1 > x2) (mk ms.seq 0).seq\n⊢ ∀ (a : ℝ) (b : MultiseriesExpansion basis_tl), (a, b) ∈ ms.seq → b.Sorted"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Tactic.ComputeAsymptotics.Multiseries.Defs | {
"line": 487,
"column": 6
} | {
"line": 487,
"column": 17
} | {
"line": 487,
"column": 18
} | [
{
"pp": "case seq.h_Pairwise\nbasis_hd : ℝ → ℝ\nbasis_tl : Basis\nms : MultiseriesExpansion (basis_hd :: basis_tl)\nh_coef : ∀ x ∈ (mk ms.seq 0).seq, x.2.Sorted\nh_Pairwise : Seq.Pairwise (fun x1 x2 ↦ x1 > x2) (mk ms.seq 0).seq\n⊢ Seq.Pairwise (fun x1 x2 ↦ x1 > x2) ms.seq",
"ppTerm": "?seq.h_Pairwise",
... | [
"case seq.h_Pairwise\nbasis_hd : ℝ → ℝ\nbasis_tl : Basis\nms : MultiseriesExpansion (basis_hd :: basis_tl)\nh_coef : ∀ x ∈ (mk ms.seq 0).seq, x.2.Sorted\nh_Pairwise : Seq.Pairwise (fun x1 x2 ↦ x1 > x2) (mk ms.seq 0).seq\n⊢ Seq.Pairwise (fun x1 x2 ↦ x2 < x1) ms.seq"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Tactic.ComputeAsymptotics.Multiseries.Monomial.Basic | {
"line": 296,
"column": 70
} | {
"line": 296,
"column": 81
} | {
"line": 296,
"column": 82
} | [
{
"pp": "exps_hd : ℝ\nexps_tl : List ℝ\nbasis_hd : ℝ → ℝ\nbasis_tl : List (ℝ → ℝ)\nh_basis : WellFormedBasis (basis_hd :: basis_tl)\nh_length : (exps_hd :: exps_tl).length = (basis_hd :: basis_tl).length\nh : exps_hd = 0 ∧ FirstNonzeroIsPos exps_tl\nh_eq : toFun (exps_hd :: exps_tl) (basis_hd :: basis_tl) = toF... | [
"exps_hd : ℝ\nexps_tl : List ℝ\nbasis_hd : ℝ → ℝ\nbasis_tl : List (ℝ → ℝ)\nh_basis : WellFormedBasis (basis_hd :: basis_tl)\nh_length : (exps_hd :: exps_tl).length = (basis_hd :: basis_tl).length\nh : exps_hd = 0 ∧ FirstNonzeroIsPos exps_tl\nh_eq : toFun (exps_hd :: exps_tl) (basis_hd :: basis_tl) = toFun exps_tl b... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Tactic.ComputeAsymptotics.Multiseries.Monomial.Basic | {
"line": 315,
"column": 71
} | {
"line": 315,
"column": 82
} | {
"line": 315,
"column": 83
} | [
{
"pp": "exps_hd : ℝ\nexps_tl : List ℝ\nbasis_hd : ℝ → ℝ\nbasis_tl : List (ℝ → ℝ)\nh_basis : WellFormedBasis (basis_hd :: basis_tl)\nh_length : (exps_hd :: exps_tl).length = (basis_hd :: basis_tl).length\nh : exps_hd = 0 ∧ FirstNonzeroIsNeg exps_tl\nh_eq : toFun (exps_hd :: exps_tl) (basis_hd :: basis_tl) = toF... | [
"exps_hd : ℝ\nexps_tl : List ℝ\nbasis_hd : ℝ → ℝ\nbasis_tl : List (ℝ → ℝ)\nh_basis : WellFormedBasis (basis_hd :: basis_tl)\nh_length : (exps_hd :: exps_tl).length = (basis_hd :: basis_tl).length\nh : exps_hd = 0 ∧ FirstNonzeroIsNeg exps_tl\nh_eq : toFun (exps_hd :: exps_tl) (basis_hd :: basis_tl) = toFun exps_tl b... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Tactic.ComputeAsymptotics.Multiseries.Defs | {
"line": 515,
"column": 43
} | {
"line": 515,
"column": 66
} | {
"line": 515,
"column": 67
} | [
{
"pp": "basis_hd : ℝ → ℝ\nbasis_tl : Basis\nexp : ℝ\ncoef : MultiseriesExpansion basis_tl\nh_coef : coef.Sorted\nexp✝ : ℝ\ncoef✝ : MultiseriesExpansion basis_tl\ntl✝ : Multiseries basis_hd basis_tl\nh_comp : (Multiseries.cons exp✝ coef✝ tl✝).leadingExp < ↑exp\nh_tl_coef : ∀ x ∈ (mk (Multiseries.cons exp✝ coef✝... | [
"basis_hd : ℝ → ℝ\nbasis_tl : Basis\nexp : ℝ\ncoef : MultiseriesExpansion basis_tl\nh_coef : coef.Sorted\nexp✝ : ℝ\ncoef✝ : MultiseriesExpansion basis_tl\ntl✝ : Multiseries basis_hd basis_tl\nh_comp : (Multiseries.cons exp✝ coef✝ tl✝).leadingExp < ↑exp\nh_tl_coef : ∀ x ∈ (mk (Multiseries.cons exp✝ coef✝ tl✝) 0).seq... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Tactic.ComputeAsymptotics.Multiseries.Defs | {
"line": 524,
"column": 4
} | {
"line": 524,
"column": 15
} | {
"line": 524,
"column": 16
} | [
{
"pp": "case seq.left\nbasis_hd : ℝ → ℝ\nbasis_tl : Basis\nexp : ℝ\ncoef : MultiseriesExpansion basis_tl\ntl : Multiseries basis_hd basis_tl\nh_coef : ∀ x ∈ (mk (Multiseries.cons exp coef tl) 0).seq, x.2.Sorted\nh_Pairwise : Seq.Pairwise (fun x1 x2 ↦ x1 > x2) (mk (Multiseries.cons exp coef tl) 0).seq\n⊢ coef.S... | [
"case seq.left\nbasis_hd : ℝ → ℝ\nbasis_tl : Basis\nexp : ℝ\ncoef : MultiseriesExpansion basis_tl\ntl : Multiseries basis_hd basis_tl\nh_coef : ∀ x ∈ (mk (Multiseries.cons exp coef tl) 0).seq, x.2.Sorted\nh_Pairwise : Seq.Pairwise (fun x1 x2 ↦ x1 > x2) (mk (Multiseries.cons exp coef tl) 0).seq\n⊢ coef.Sorted"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Tactic.ComputeAsymptotics.Multiseries.Monomial.Basic | {
"line": 353,
"column": 43
} | {
"line": 353,
"column": 54
} | {
"line": 353,
"column": 55
} | [
{
"pp": "basis_hd : ℝ → ℝ\nbasis_tl : List (ℝ → ℝ)\nh_basis : WellFormedBasis (basis_hd :: basis_tl)\nexp1 : ℝ\nm1 : List ℝ\nh1 : (exp1 :: m1).length = (basis_hd :: basis_tl).length\nm2 : List ℝ\nh2 : (exp1 :: m2).length = (basis_hd :: basis_tl).length\nh : List.Lex (fun x1 x2 ↦ x1 < x2) m1 m2\n⊢ m1.length = ba... | [
"basis_hd : ℝ → ℝ\nbasis_tl : List (ℝ → ℝ)\nh_basis : WellFormedBasis (basis_hd :: basis_tl)\nexp1 : ℝ\nm1 : List ℝ\nh1 : (exp1 :: m1).length = (basis_hd :: basis_tl).length\nm2 : List ℝ\nh2 : (exp1 :: m2).length = (basis_hd :: basis_tl).length\nh : List.Lex (fun x1 x2 ↦ x1 < x2) m1 m2\n⊢ m1.length = basis_tl.lengt... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Tactic.ComputeAsymptotics.Multiseries.Monomial.Basic | {
"line": 353,
"column": 63
} | {
"line": 353,
"column": 74
} | {
"line": 353,
"column": 75
} | [
{
"pp": "basis_hd : ℝ → ℝ\nbasis_tl : List (ℝ → ℝ)\nh_basis : WellFormedBasis (basis_hd :: basis_tl)\nexp1 : ℝ\nm1 : List ℝ\nh1 : (exp1 :: m1).length = (basis_hd :: basis_tl).length\nm2 : List ℝ\nh2 : (exp1 :: m2).length = (basis_hd :: basis_tl).length\nh : List.Lex (fun x1 x2 ↦ x1 < x2) m1 m2\n⊢ m2.length = ba... | [
"basis_hd : ℝ → ℝ\nbasis_tl : List (ℝ → ℝ)\nh_basis : WellFormedBasis (basis_hd :: basis_tl)\nexp1 : ℝ\nm1 : List ℝ\nh1 : (exp1 :: m1).length = (basis_hd :: basis_tl).length\nm2 : List ℝ\nh2 : (exp1 :: m2).length = (basis_hd :: basis_tl).length\nh : List.Lex (fun x1 x2 ↦ x1 < x2) m1 m2\n⊢ m2.length = basis_tl.lengt... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Tactic.ComputeAsymptotics.Multiseries.Monomial.Basic | {
"line": 353,
"column": 63
} | {
"line": 353,
"column": 77
} | {
"line": 353,
"column": 77
} | [
{
"pp": "basis_hd : ℝ → ℝ\nbasis_tl : List (ℝ → ℝ)\nh_basis : WellFormedBasis (basis_hd :: basis_tl)\nexp1 : ℝ\nm1 : List ℝ\nh1 : (exp1 :: m1).length = (basis_hd :: basis_tl).length\nm2 : List ℝ\nh2 : (exp1 :: m2).length = (basis_hd :: basis_tl).length\nh : List.Lex (fun x1 x2 ↦ x1 < x2) m1 m2\n⊢ m2.length = ba... | [] | simpa using h2 | Lean.Elab.Tactic.Simpa.evalSimpa | Lean.Parser.Tactic.simpa |
Mathlib.Tactic.ComputeAsymptotics.Multiseries.Monomial.Basic | {
"line": 353,
"column": 63
} | {
"line": 353,
"column": 77
} | {
"line": 353,
"column": 77
} | [
{
"pp": "basis_hd : ℝ → ℝ\nbasis_tl : List (ℝ → ℝ)\nh_basis : WellFormedBasis (basis_hd :: basis_tl)\nexp1 : ℝ\nm1 : List ℝ\nh1 : (exp1 :: m1).length = (basis_hd :: basis_tl).length\nm2 : List ℝ\nh2 : (exp1 :: m2).length = (basis_hd :: basis_tl).length\nh : List.Lex (fun x1 x2 ↦ x1 < x2) m1 m2\n⊢ m2.length = ba... | [] | simpa using h2 | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Tactic.ComputeAsymptotics.Multiseries.Monomial.Basic | {
"line": 353,
"column": 63
} | {
"line": 353,
"column": 77
} | {
"line": 353,
"column": 77
} | [
{
"pp": "basis_hd : ℝ → ℝ\nbasis_tl : List (ℝ → ℝ)\nh_basis : WellFormedBasis (basis_hd :: basis_tl)\nexp1 : ℝ\nm1 : List ℝ\nh1 : (exp1 :: m1).length = (basis_hd :: basis_tl).length\nm2 : List ℝ\nh2 : (exp1 :: m2).length = (basis_hd :: basis_tl).length\nh : List.Lex (fun x1 x2 ↦ x1 < x2) m1 m2\n⊢ m2.length = ba... | [] | simpa using h2 | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Tactic.ComputeAsymptotics.Multiseries.Defs | {
"line": 538,
"column": 24
} | {
"line": 538,
"column": 35
} | {
"line": 538,
"column": 36
} | [
{
"pp": "case cons\nbasis_hd : ℝ → ℝ\nbasis_tl : Basis\nexp : ℝ\ncoef : MultiseriesExpansion basis_tl\ntl : Multiseries basis_hd basis_tl\nh : (Multiseries.cons exp coef tl).Sorted\n⊢ (Multiseries.cons exp coef tl).tail.Sorted",
"ppTerm": "?cons",
"assigned": true,
"usedConstants": [
"Eq.mpr",... | [
"case cons\nbasis_hd : ℝ → ℝ\nbasis_tl : Basis\nexp : ℝ\ncoef : MultiseriesExpansion basis_tl\ntl : Multiseries basis_hd basis_tl\nh : (Multiseries.cons exp coef tl).Sorted\n⊢ tl.Sorted"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Tactic.ComputeAsymptotics.Multiseries.Monomial.Basic | {
"line": 367,
"column": 8
} | {
"line": 367,
"column": 39
} | {
"line": 368,
"column": 8
} | [
{
"pp": "case cons.cons.cons.rel.h.h_firstIsPos\nbasis_hd : ℝ → ℝ\nbasis_tl : List (ℝ → ℝ)\nh_basis : WellFormedBasis (basis_hd :: basis_tl)\nexp1 : ℝ\nm1 : List ℝ\nexp2 : ℝ\nm2 : List ℝ\nh : exp1 < exp2\nh1 : m1.length = basis_tl.length\nh2 : m2.length = basis_tl.length\n⊢ FirstNonzeroIsPos ((exp2 - exp1) :: m... | [
"case cons.cons.cons.rel.h.h_firstIsPos\nbasis_hd : ℝ → ℝ\nbasis_tl : List (ℝ → ℝ)\nh_basis : WellFormedBasis (basis_hd :: basis_tl)\nexp1 : ℝ\nm1 : List ℝ\nexp2 : ℝ\nm2 : List ℝ\nh : exp1 < exp2\nh1 : m1.length = basis_tl.length\nh2 : m2.length = basis_tl.length\n⊢ 0 < exp2 - exp1"
] | apply FirstNonzeroIsPos.of_head | Lean.Elab.Tactic.evalApply | Lean.Parser.Tactic.apply |
Mathlib.Tactic.ComputeAsymptotics.Multiseries.Defs | {
"line": 599,
"column": 41
} | {
"line": 599,
"column": 52
} | {
"line": 599,
"column": 53
} | [
{
"pp": "basis_hd : ℝ → ℝ\nbasis_tl : Basis\nexp : ℝ\ncoef : MultiseriesExpansion basis_tl\ntl : Multiseries basis_hd basis_tl\nf : ℝ → ℝ\nh : (mk (Multiseries.cons exp coef tl) f).Sorted\n⊢ (Multiseries.cons exp coef tl).Sorted",
"ppTerm": "?m.19",
"assigned": false,
"usedConstants": [],
"usedF... | [
"basis_hd : ℝ → ℝ\nbasis_tl : Basis\nexp : ℝ\ncoef : MultiseriesExpansion basis_tl\ntl : Multiseries basis_hd basis_tl\nf : ℝ → ℝ\nh : (mk (Multiseries.cons exp coef tl) f).Sorted\n⊢ (Multiseries.cons exp coef tl).Sorted"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Tactic.ComputeAsymptotics.Multiseries.Defs | {
"line": 604,
"column": 2
} | {
"line": 604,
"column": 13
} | {
"line": 604,
"column": 14
} | [
{
"pp": "basis_hd : ℝ → ℝ\nbasis_tl : Basis\nms : MultiseriesExpansion (basis_hd :: basis_tl)\nf : ℝ → ℝ\nh_sorted : ms.Sorted\n⊢ (ms.replaceFun f).Sorted",
"ppTerm": "?m.6",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Tactic.ComputeAsymptotics.MultiseriesExpansion.sorted_iff_seq_sor... | [
"basis_hd : ℝ → ℝ\nbasis_tl : Basis\nms : MultiseriesExpansion (basis_hd :: basis_tl)\nf : ℝ → ℝ\nh_sorted : ms.Sorted\n⊢ ms.seq.Sorted"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Tactic.ComputeAsymptotics.Multiseries.Trimming | {
"line": 62,
"column": 11
} | {
"line": 62,
"column": 22
} | {
"line": 62,
"column": 23
} | [
{
"pp": "case nil\nbasis_hd✝ : ℝ → ℝ\nbasis_tl✝ : List (ℝ → ℝ)\nf✝ : ℝ → ℝ\nh_approx : (mk Multiseries.nil f✝).Approximates\n⊢ (mk Multiseries.nil f✝).toFun =ᶠ[atTop] 0",
"ppTerm": "?nil",
"assigned": true,
"usedConstants": [
"Real",
"Real.instZero",
"Filter.EventuallyEq",
"i... | [
"case nil\nbasis_hd✝ : ℝ → ℝ\nbasis_tl✝ : List (ℝ → ℝ)\nf✝ : ℝ → ℝ\nh_approx : (mk Multiseries.nil f✝).Approximates\n⊢ f✝ =ᶠ[atTop] 0"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Tactic.ComputeAsymptotics.Multiseries.Trimming | {
"line": 122,
"column": 2
} | {
"line": 126,
"column": 9
} | {
"line": 128,
"column": 0
} | [
{
"pp": "basis_hd : ℝ → ℝ\nbasis_tl : Basis\nexp : ℝ\ncoef : MultiseriesExpansion basis_tl\ntl ms : Multiseries basis_hd basis_tl\nh_ms : Multiseries.cons exp coef tl = ms\nh : ms.Trimmed\n⊢ coef.Trimmed ∧ ¬coef.IsZero",
"ppTerm": "?m.16",
"assigned": true,
"usedConstants": [
"Stream'.Seq",
... | [] | cases h with
| nil => simp at h_ms
| cons h_trimmed h_ne_zero =>
simp at h_ms
grind | _private.Lean.Elab.Tactic.Induction.0.Lean.Elab.Tactic.evalCases | Lean.Parser.Tactic.cases |
Mathlib.Tactic.DeriveCountable | {
"line": 83,
"column": 2
} | {
"line": 83,
"column": 41
} | {
"line": 83,
"column": 42
} | [
{
"pp": "p : Prop\na b b' : ℕ\nh : b = b' → p\n⊢ Nat.pair a b = Nat.pair a b' → p",
"ppTerm": "?m.3",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Nat.pair_eq_pair._simp_1",
"congrArg",
"id",
"Nat.pair",
"And",
"implies_congr",
"Nat",
"True",
... | [
"p : Prop\na b b' : ℕ\nh : b = b' → p\n⊢ b = b' → p"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Tactic.ComputeAsymptotics.Multiseries.Corecursion | {
"line": 451,
"column": 6
} | {
"line": 451,
"column": 58
} | {
"line": 451,
"column": 59
} | [
{
"pp": "case succ.some\nα : Type u_1\nmotive : (Stream'.Seq α → Stream'.Seq α) → Prop\nh_step :\n ∀ (op : Stream'.Seq α → Stream'.Seq α),\n motive op →\n ∃ T,\n ∀ (s : Stream'.Seq α),\n (op s).destruct =\n Option.map\n (fun x ↦\n match x with\n ... | [
"case succ.some\nα : Type u_1\nmotive : (Stream'.Seq α → Stream'.Seq α) → Prop\nh_step :\n ∀ (op : Stream'.Seq α → Stream'.Seq α),\n motive op →\n ∃ T,\n ∀ (s : Stream'.Seq α),\n (op s).destruct =\n Option.map\n (fun x ↦\n match x with\n ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.SetTheory.Ordinal.Notation | {
"line": 1074,
"column": 8
} | {
"line": 1074,
"column": 56
} | {
"line": 1075,
"column": 8
} | [
{
"pp": "case oadd.inl.none.inl.some.succ.refine_2\na : ONote\nm : ℕ+\nb : ONote\nihb : b = 0\ne✝ : b.fundamentalSequence = Sum.inl none\na' : ONote\niha : a.repr = succ a'.repr ∧ (a.NF → a'.NF)\ne : a.fundamentalSequence = Sum.inl (some a')\nm' : ℕ\ne' : m.natPred = m' + 1\nthis : 0 < ω ^ a'.repr\ni : ℕ\nH : (... | [
"case oadd.inl.none.inl.some.succ.refine_2\na : ONote\nm : ℕ+\nb : ONote\nihb : b = 0\ne✝ : b.fundamentalSequence = Sum.inl none\na' : ONote\niha : a.repr = succ a'.repr ∧ (a.NF → a'.NF)\ne : a.fundamentalSequence = Sum.inl (some a')\nm' : ℕ\ne' : m.natPred = m' + 1\nthis : 0 < ω ^ a'.repr\ni : ℕ\nH : (a.oadd (m' +... | rw [repr, repr_zero, add_zero, iha.1, opow_succ] | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_rwSeq_1 | Lean.Parser.Tactic.rwSeq |
Mathlib.Tactic.ComputeAsymptotics.Multiseries.Corecursion | {
"line": 532,
"column": 4
} | {
"line": 532,
"column": 40
} | {
"line": 533,
"column": 4
} | [
{
"pp": "case h.nil\nα : Type u_1\nmotive : (Stream'.Seq α → Stream'.Seq α) → Prop\nh_step :\n ∀ (op : Stream'.Seq α → Stream'.Seq α),\n motive op →\n ∃ T,\n ∀ (s : Stream'.Seq α),\n (op s).destruct =\n Option.map\n (fun x ↦\n match x with\n ... | [
"case h.nil\nα : Type u_1\nmotive : (Stream'.Seq α → Stream'.Seq α) → Prop\nh_step :\n ∀ (op : Stream'.Seq α → Stream'.Seq α),\n motive op →\n ∃ T,\n ∀ (s : Stream'.Seq α),\n (op s).destruct =\n Option.map\n (fun x ↦\n match x with\n | (... | simp only [tail_nil, head_nil] at hT | Lean.Elab.Tactic.evalSimp | Lean.Parser.Tactic.simp |
Mathlib.Tactic.ComputeAsymptotics.Multiseries.Corecursion | {
"line": 557,
"column": 27
} | {
"line": 557,
"column": 38
} | {
"line": 557,
"column": 39
} | [
{
"pp": "α : Type u_1\nγ : Type u_3\ns t : Stream'.Seq α\nop : γ → Stream'.Seq α → Stream'.Seq α\ninst✝ : FriendlyOperationClass op\nmotive : Stream'.Seq α → Stream'.Seq α → Prop\nbase : motive s t\nstep :\n ∀ (u v : Stream'.Seq α),\n motive u v → u = v ∨ ∃ hd u' v' c, u = Seq.cons hd (op c u') ∧ v = Seq.co... | [
"α : Type u_1\nγ : Type u_3\ns t : Stream'.Seq α\nop : γ → Stream'.Seq α → Stream'.Seq α\ninst✝ : FriendlyOperationClass op\nmotive : Stream'.Seq α → Stream'.Seq α → Prop\nbase : motive s t\nstep :\n ∀ (u v : Stream'.Seq α),\n motive u v → u = v ∨ ∃ hd u' v' c, u = Seq.cons hd (op c u') ∧ v = Seq.cons hd (op c ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Tactic.ComputeAsymptotics.Multiseries.Corecursion | {
"line": 576,
"column": 15
} | {
"line": 577,
"column": 27
} | {
"line": 579,
"column": 0
} | [
{
"pp": "α : Type u_1\nγ : Type u_3\nop : γ → Stream'.Seq α → Stream'.Seq α\ninst✝ : FriendlyOperationClass op\nmotive : Stream'.Seq α → Stream'.Seq α → Prop\nstep :\n ∀ (u v : Stream'.Seq α),\n motive u v → u = v ∨ ∃ hd u' v' c, u = Seq.cons hd (op c u') ∧ v = Seq.cons hd (op c v') ∧ motive u' v'\nn : ℕ\nh... | [] | by
grw [ih, pow_succ'] | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.Tactic.NormNum.Irrational | {
"line": 55,
"column": 4
} | {
"line": 55,
"column": 24
} | {
"line": 55,
"column": 25
} | [
{
"pp": "case inl\np q : ℕ\nh_coprime : p.Coprime q\nhq : 0 < q\nm : ℕ\nh : ∀ (m : ℕ), 0 ≠ m ^ q\n⊢ 0 ^ p ≠ m ^ q",
"ppTerm": "?inl",
"assigned": true,
"usedConstants": [
"Nat.instMonoid",
"id",
"Ne",
"instOfNatNat",
"NPow.toPow",
"HPow.hPow",
"Nat",
"... | [
"case inl\np q : ℕ\nh_coprime : p.Coprime q\nhq : 0 < q\nm : ℕ\nh : ∀ (m : ℕ), 0 ≠ m ^ q\n⊢ ¬0 ^ p = m ^ q"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Tactic.NormNum.Irrational | {
"line": 59,
"column": 29
} | {
"line": 59,
"column": 49
} | {
"line": 59,
"column": 50
} | [
{
"pp": "n p q : ℕ\nh_coprime : p.Coprime q\nhq : 0 < q\nm : ℕ\nhn : n ≠ 0\nh : n ^ p = m ^ q\nf : ℕ →₀ ℕ := Finsupp.mapRange (fun x ↦ x / q) ⋯ n.factorization\nhf : n.factorization = q • f\n⊢ f 0 = 0",
"ppTerm": "?m.86",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": ... | [
"n p q : ℕ\nh_coprime : p.Coprime q\nhq : 0 < q\nm : ℕ\nhn : n ≠ 0\nh : n ^ p = m ^ q\nf : ℕ →₀ ℕ := Finsupp.mapRange (fun x ↦ x / q) ⋯ n.factorization\nhf : n.factorization = q • f\n⊢ f 0 = 0"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Tactic.NormNum.LegendreSymbol | {
"line": 75,
"column": 98
} | {
"line": 81,
"column": 41
} | {
"line": 83,
"column": 0
} | [
{
"pp": "b : ℕ\nhb : (b / 2).beq 0 = false\n⊢ jacobiSymNat 0 b = 0",
"ppTerm": "?m.15",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Trans.trans",
"instHDiv",
"HMul.hMul",
"Nat.ne_of_beq_eq_false",
"of_decide_eq_true",
"congrArg",
"Nat.succ_le_of_lt... | [] | by
rw [jacobiSymNat, Nat.cast_zero, jacobiSym.zero_left ?_]
calc
1 < 2 * 1 := by decide
_ ≤ 2 * (b / 2) :=
Nat.mul_le_mul_left _ (Nat.succ_le_of_lt (Nat.pos_of_ne_zero (Nat.ne_of_beq_eq_false hb)))
_ ≤ b := Nat.mul_div_le b 2 | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.Tactic.NormNum.Irrational | {
"line": 65,
"column": 2
} | {
"line": 65,
"column": 13
} | {
"line": 65,
"column": 14
} | [
{
"pp": "case inr\nn p q : ℕ\nh_coprime : p.Coprime q\nhq : 0 < q\nm : ℕ\nhn : n ≠ 0\nh : n ^ p = m ^ q\nf : ℕ →₀ ℕ := Finsupp.mapRange (fun x ↦ x / q) ⋯ n.factorization\nz : ℕ\n⊢ q ∣ n.factorization z",
"ppTerm": "?inr✝",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals":... | [
"case inr\nn p q : ℕ\nh_coprime : p.Coprime q\nhq : 0 < q\nm : ℕ\nhn : n ≠ 0\nh : n ^ p = m ^ q\nf : ℕ →₀ ℕ := Finsupp.mapRange (fun x ↦ x / q) ⋯ n.factorization\nz : ℕ\n⊢ q ∣ n.factorization z"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Tactic.NormNum.Irrational | {
"line": 65,
"column": 56
} | {
"line": 65,
"column": 67
} | {
"line": 65,
"column": 68
} | [
{
"pp": "n p q : ℕ\nh_coprime : p.Coprime q\nhq : 0 < q\nm : ℕ\nhn : n ≠ 0\nh : n ^ p = m ^ q\nf : ℕ →₀ ℕ := Finsupp.mapRange (fun x ↦ x / q) ⋯ n.factorization\nz : ℕ\n⊢ p * n.factorization z = q * ?m.185",
"ppTerm": "?m.186",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoa... | [
"n p q : ℕ\nh_coprime : p.Coprime q\nhq : 0 < q\nm : ℕ\nhn : n ≠ 0\nh : n ^ p = m ^ q\nf : ℕ →₀ ℕ := Finsupp.mapRange (fun x ↦ x / q) ⋯ n.factorization\nz : ℕ\n⊢ p * n.factorization z = q * ?m.185"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Tactic.NormNum.Irrational | {
"line": 125,
"column": 2
} | {
"line": 125,
"column": 19
} | {
"line": 125,
"column": 20
} | [
{
"pp": "a b d : ℕ\nh_coprime : a.Coprime b\nq : ℚ\nhq : 0 ≤ q\nhb_zero : ¬b = 0\nx' : ℤ := ⋯\ny : ℕ := ⋯\nx : ℕ\nha : a ≠ x ^ d\nhx' : x' = ↑x\nh : a * y ^ d = b * x ^ d\n⊢ x.Coprime y",
"ppTerm": "?m.203",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"a b d : ℕ\nh_coprime : a.Coprime b\nq : ℚ\nhq : 0 ≤ q\nhb_zero : ¬b = 0\nx' : ℤ := ⋯\ny : ℕ := ⋯\nx : ℕ\nha : a ≠ x ^ d\nhx' : x' = ↑x\nh : a * y ^ d = b * x ^ d\n⊢ x.Coprime y"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Tactic.NormNum.Irrational | {
"line": 179,
"column": 2
} | {
"line": 179,
"column": 71
} | {
"line": 180,
"column": 2
} | [
{
"pp": "x y : ℝ\nx_num x_den y_num y_den k_den : ℕ\nhy_isNNRat : IsNNRat y y_num y_den\nhx_coprime : x_num.Coprime x_den\nhy_coprime : y_num.Coprime y_den\nhd1 : k_den ^ y_den < x_den\nhd2 : x_den < (k_den + 1) ^ y_den\nhx_inv : Invertible ↑x_den\nhx_eq : x = ↑x_num * ⅟↑x_den\n⊢ Irrational (x ^ y)⁻¹",
"ppT... | [
"x y : ℝ\nx_num x_den y_num y_den k_den : ℕ\nhy_isNNRat : IsNNRat y y_num y_den\nhx_coprime : x_num.Coprime x_den\nhy_coprime : y_num.Coprime y_den\nhd1 : k_den ^ y_den < x_den\nhd2 : x_den < (k_den + 1) ^ y_den\nhx_inv : Invertible ↑x_den\nhx_eq : x = ↑x_num * ⅟↑x_den\n⊢ Irrational (x⁻¹ ^ y)"
] | rw [← Real.inv_rpow (by simp only [hx_eq, invOf_eq_inv]; positivity)] | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_rwSeq_1 | Lean.Parser.Tactic.rwSeq |
Mathlib.Tactic.NormNum.RealSqrt | {
"line": 46,
"column": 2
} | {
"line": 46,
"column": 89
} | {
"line": 46,
"column": 90
} | [
{
"pp": "num denom : ℕ\ninv : Invertible ↑denom\nh₁ : 0 ≤ ↑↑num * ⅟↑denom\n⊢ √(↑(Int.negOfNat num) * ⅟↑denom) = ↑0",
"ppTerm": "?m.63",
"assigned": true,
"usedConstants": [
"AddGroup.toSubtractionMonoid",
"Int.cast",
"Eq.mpr",
"NegZeroClass.toNeg",
"Real.instLE",
... | [
"num denom : ℕ\ninv : Invertible ↑denom\nh₁ : 0 ≤ ↑↑num * ⅟↑denom\n⊢ 0 ≤ ↑num * (↑denom)⁻¹"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Tactic.Simproc.FinsetInterval | {
"line": 27,
"column": 69
} | {
"line": 27,
"column": 80
} | {
"line": 27,
"column": 81
} | [
{
"pp": "m n : ℕ\nhnm : n.blt m = true\n⊢ Icc m n = ∅",
"ppTerm": "?m.8",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Preorder.toLT",
"Finset",
"PartialOrder.toPreorder",
"Preorder.toLE",
"Nat.instLocallyFiniteOrder",
"id",
"Finset.Icc_eq_empty_iff... | [
"m n : ℕ\nhnm : n.blt m = true\n⊢ n < m"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Tactic.Simproc.FinsetInterval | {
"line": 30,
"column": 76
} | {
"line": 30,
"column": 87
} | {
"line": 30,
"column": 88
} | [
{
"pp": "m n : ℕ\ns : Finset ℕ\nhmn : m.ble n = true\nhs : Icc (m + 1) n = s\n⊢ m ≤ n",
"ppTerm": "?m.29",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"m n : ℕ\ns : Finset ℕ\nhmn : m.ble n = true\nhs : Icc (m + 1) n = s\n⊢ m ≤ n"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Tactic.Simproc.FinsetInterval | {
"line": 55,
"column": 67
} | {
"line": 55,
"column": 78
} | {
"line": 55,
"column": 79
} | [
{
"pp": "m n : ℤ\nhnm : n < m\n⊢ Icc m n = ∅",
"ppTerm": "?m.9",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Preorder.toLT",
"Int.instLinearOrder",
"Finset",
"PartialOrder.toPreorder",
"Preorder.toLE",
"SemilatticeInf.toPartialOrder",
"id",
"... | [
"m n : ℤ\nhnm : n < m\n⊢ n < m"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Tactic.Simproc.FinsetInterval | {
"line": 58,
"column": 76
} | {
"line": 58,
"column": 87
} | {
"line": 58,
"column": 88
} | [
{
"pp": "m n : ℤ\ns : Finset ℤ\nhmn : m ≤ n\nhs : Icc (m + 1) n = s\n⊢ m ≤ n",
"ppTerm": "?m.30",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"m n : ℤ\ns : Finset ℤ\nhmn : m ≤ n\nhs : Icc (m + 1) n = s\n⊢ m ≤ n"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Testing.Plausible.Functions | {
"line": 114,
"column": 8
} | {
"line": 114,
"column": 19
} | {
"line": 114,
"column": 20
} | [
{
"pp": "case mp\nα : Type u\nβ : Type v\ninst✝² : DecidableEq α\ninst✝¹ : Zero β\ninst✝ : DecidableEq β\na : α\nA : List ((_ : α) × β)\ny od : β\nhval : ⟨a, od⟩ ∈ A.dedupKeys\nhod : (decide ¬od = 0) = true\nthis : od ∈ List.dlookup a A.dedupKeys\n⊢ ¬(some od).getD 0 = 0",
"ppTerm": "?mp",
"assigned": t... | [
"case mp\nα : Type u\nβ : Type v\ninst✝² : DecidableEq α\ninst✝¹ : Zero β\ninst✝ : DecidableEq β\na : α\nA : List ((_ : α) × β)\ny od : β\nhval : ⟨a, od⟩ ∈ A.dedupKeys\nhod : (decide ¬od = 0) = true\nthis : od ∈ List.dlookup a A.dedupKeys\n⊢ ¬od = 0"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Topology.Algebra.Group.OpenMapping | {
"line": 63,
"column": 8
} | {
"line": 63,
"column": 44
} | {
"line": 63,
"column": 45
} | [
{
"pp": "G : Type u_1\nX : Type u_2\ninst✝⁹ : TopologicalSpace G\ninst✝⁸ : TopologicalSpace X\ninst✝⁷ : Group G\ninst✝⁶ : IsTopologicalGroup G\ninst✝⁵ : MulAction G X\ninst✝⁴ : SigmaCompactSpace G\ninst✝³ : BaireSpace X\ninst✝² : T2Space X\ninst✝¹ : ContinuousSMul G X\ninst✝ : IsPretransitive G X\nU : Set G\nhU... | [
"G : Type u_1\nX : Type u_2\ninst✝⁹ : TopologicalSpace G\ninst✝⁸ : TopologicalSpace X\ninst✝⁷ : Group G\ninst✝⁶ : IsTopologicalGroup G\ninst✝⁵ : MulAction G X\ninst✝⁴ : SigmaCompactSpace G\ninst✝³ : BaireSpace X\ninst✝² : T2Space X\ninst✝¹ : ContinuousSMul G X\ninst✝ : IsPretransitive G X\nU : Set G\nhU : U ∈ 𝓝 1\... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Topology.Algebra.Group.OpenMapping | {
"line": 80,
"column": 53
} | {
"line": 80,
"column": 64
} | {
"line": 80,
"column": 65
} | [
{
"pp": "G : Type u_1\nX : Type u_2\ninst✝⁹ : TopologicalSpace G\ninst✝⁸ : TopologicalSpace X\ninst✝⁷ : Group G\ninst✝⁶ : IsTopologicalGroup G\ninst✝⁵ : MulAction G X\ninst✝⁴ : SigmaCompactSpace G\ninst✝³ : BaireSpace X\ninst✝² : T2Space X\ninst✝¹ : ContinuousSMul G X\ninst✝ : IsPretransitive G X\nU : Set G\nhU... | [
"G : Type u_1\nX : Type u_2\ninst✝⁹ : TopologicalSpace G\ninst✝⁸ : TopologicalSpace X\ninst✝⁷ : Group G\ninst✝⁶ : IsTopologicalGroup G\ninst✝⁵ : MulAction G X\ninst✝⁴ : SigmaCompactSpace G\ninst✝³ : BaireSpace X\ninst✝² : T2Space X\ninst✝¹ : ContinuousSMul G X\ninst✝ : IsPretransitive G X\nU : Set G\nhU : U ∈ 𝓝 1\... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Topology.Algebra.Group.SubmonoidClosure | {
"line": 54,
"column": 2
} | {
"line": 54,
"column": 13
} | {
"line": 54,
"column": 14
} | [
{
"pp": "G : Type u_1\ninst✝³ : Group G\ninst✝² : TopologicalSpace G\ninst✝¹ : CompactSpace G\ninst✝ : IsTopologicalGroup G\nx : G\n⊢ MapClusterPt 1 atTop fun x_1 ↦ x ^ x_1",
"ppTerm": "?m.16",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"G : Type u_1\ninst✝³ : Group G\ninst✝² : TopologicalSpace G\ninst✝¹ : CompactSpace G\ninst✝ : IsTopologicalGroup G\nx : G\n⊢ MapClusterPt 1 atTop fun x_1 ↦ x ^ x_1"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Topology.Algebra.Group.SubmonoidClosure | {
"line": 58,
"column": 2
} | {
"line": 58,
"column": 13
} | {
"line": 58,
"column": 14
} | [
{
"pp": "G : Type u_1\ninst✝³ : Group G\ninst✝² : TopologicalSpace G\ninst✝¹ : CompactSpace G\ninst✝ : IsTopologicalGroup G\nx : G\n⊢ MapClusterPt x atTop fun x_1 ↦ x ^ x_1",
"ppTerm": "?m.14",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"G : Type u_1\ninst✝³ : Group G\ninst✝² : TopologicalSpace G\ninst✝¹ : CompactSpace G\ninst✝ : IsTopologicalGroup G\nx : G\n⊢ MapClusterPt x atTop fun x_1 ↦ x ^ x_1"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Topology.Algebra.Group.OpenMapping | {
"line": 108,
"column": 2
} | {
"line": 108,
"column": 13
} | {
"line": 108,
"column": 14
} | [
{
"pp": "G : Type u_1\nX : Type u_2\ninst✝⁹ : TopologicalSpace G\ninst✝⁸ : TopologicalSpace X\ninst✝⁷ : Group G\ninst✝⁶ : IsTopologicalGroup G\ninst✝⁵ : MulAction G X\ninst✝⁴ : SigmaCompactSpace G\ninst✝³ : BaireSpace X\ninst✝² : T2Space X\ninst✝¹ : ContinuousSMul G X\ninst✝ : IsPretransitive G X\nx : X\ng : G\... | [
"G : Type u_1\nX : Type u_2\ninst✝⁹ : TopologicalSpace G\ninst✝⁸ : TopologicalSpace X\ninst✝⁷ : Group G\ninst✝⁶ : IsTopologicalGroup G\ninst✝⁵ : MulAction G X\ninst✝⁴ : SigmaCompactSpace G\ninst✝³ : BaireSpace X\ninst✝² : T2Space X\ninst✝¹ : ContinuousSMul G X\ninst✝ : IsPretransitive G X\nx : X\ng : G\nU : Set G\n... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Topology.UniformSpace.Ascoli | {
"line": 429,
"column": 2
} | {
"line": 429,
"column": 59
} | {
"line": 433,
"column": 2
} | [
{
"pp": "ι : Type u_1\nX : Type u_2\nα : Type u_3\ninst✝² : TopologicalSpace X\ninst✝¹ : UniformSpace α\nF : ι → X → α\ninst✝ : TopologicalSpace ι\n𝔖 : Set (Set X)\n𝔖_compact : ∀ K ∈ 𝔖, IsCompact K\nF_ind : IsInducing (⇑(UniformOnFun.ofFun 𝔖) ∘ F)\nF_cl : IsClosed[UniformOnFun.topologicalSpace X α 𝔖] (rang... | [
"ι : Type u_1\nX : Type u_2\nα : Type u_3\ninst✝² : TopologicalSpace X\ninst✝¹ : UniformSpace α\nF : ι → X → α\ninst✝ : TopologicalSpace ι\n𝔖 : Set (Set X)\n𝔖_compact : ∀ K ∈ 𝔖, IsCompact K\nF_ind : IsInducing (⇑(UniformOnFun.ofFun 𝔖) ∘ F)\nF_cl : IsClosed[UniformOnFun.topologicalSpace X α 𝔖] (range (⇑(Uniform... | rw [← isCompact_univ_iff, this.isCompact_iff, image_univ] | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_rwSeq_1 | Lean.Parser.Tactic.rwSeq |
Mathlib.Topology.UniformSpace.Ascoli | {
"line": 499,
"column": 2
} | {
"line": 501,
"column": 64
} | {
"line": 502,
"column": 2
} | [
{
"pp": "X : Type u_2\nα : Type u_3\ninst✝¹ : TopologicalSpace X\ninst✝ : UniformSpace α\nS : Set C(X, α)\nhS1 : IsCompact (ContinuousMap.toFun '' S)\nhS2 : Equicontinuous fun x ↦ ⇑↑x\n⊢ IsCompact S",
"ppTerm": "?m.20",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Equiv.instEquivLike"... | [
"X : Type u_2\nα : Type u_3\ninst✝¹ : TopologicalSpace X\ninst✝ : UniformSpace α\nS : Set C(X, α)\nhS1 : IsCompact (ContinuousMap.toFun '' S)\nhS2 : Equicontinuous fun x ↦ ⇑↑x\n⊢ IsInducing ⇑(Equiv.Set.image DFunLike.coe S ⋯)"
] | suffices h : IsInducing (Equiv.Set.image _ S DFunLike.coe_injective) by
rw [isCompact_iff_compactSpace] at hS1 ⊢
exact (Equiv.toHomeomorphOfIsInducing _ h).symm.compactSpace | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_tacticSuffices__1 | Lean.Parser.Tactic.tacticSuffices_ |
Mathlib.Topology.Algebra.IsOpenUnits | {
"line": 78,
"column": 4
} | {
"line": 78,
"column": 81
} | {
"line": 79,
"column": 6
} | [
{
"pp": "R : Type u_1\ninst✝² : CommRing R\ninst✝¹ : TopologicalSpace R\ninst✝ : IsTopologicalRing R\nI : Ideal R\nhR : IsAdic I\nhI : I ≤ ⊥.jacobson\ns : Set R\nhs : s ∈ Filter.map (⇑(Units.coeHom R)) (Filter.comap (⇑(Units.embedProduct R)) (𝓝 1 ×ˢ 𝓝 1))\nH : (𝓝 1).HasBasis (fun _n ↦ True) fun n ↦ (fun y ↦ ... | [
"R : Type u_1\ninst✝² : CommRing R\ninst✝¹ : TopologicalSpace R\ninst✝ : IsTopologicalRing R\nI : Ideal R\nhR : IsAdic I\nhI : I ≤ ⊥.jacobson\ns : Set R\nhs : s ∈ Filter.map (⇑(Units.coeHom R)) (Filter.comap (⇑(Units.embedProduct R)) (𝓝 1 ×ˢ 𝓝 1))\nH : (𝓝 1).HasBasis (fun _n ↦ True) fun n ↦ (fun y ↦ 1 + y) '' ↑(... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Topology.Algebra.IsOpenUnits | {
"line": 91,
"column": 27
} | {
"line": 91,
"column": 38
} | {
"line": 91,
"column": 39
} | [
{
"pp": "R : Type u_1\ninst✝² : CommRing R\ninst✝¹ : TopologicalSpace R\ninst✝ : IsTopologicalRing R\nI : Ideal R\nhR : IsAdic I\nhI : I ≤ ⊥.jacobson\ns : Set R\nhs : s ∈ Filter.map (⇑(Units.coeHom R)) (Filter.comap (⇑(Units.embedProduct R)) (𝓝 1 ×ˢ 𝓝 1))\nH : (𝓝 1).HasBasis (fun _n ↦ True) fun n ↦ (fun y ↦ ... | [
"R : Type u_1\ninst✝² : CommRing R\ninst✝¹ : TopologicalSpace R\ninst✝ : IsTopologicalRing R\nI : Ideal R\nhR : IsAdic I\nhI : I ≤ ⊥.jacobson\ns : Set R\nhs : s ∈ Filter.map (⇑(Units.coeHom R)) (Filter.comap (⇑(Units.embedProduct R)) (𝓝 1 ×ˢ 𝓝 1))\nH : (𝓝 1).HasBasis (fun _n ↦ True) fun n ↦ (fun y ↦ 1 + y) '' ↑(... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Topology.Algebra.Nonarchimedean.TotallyDisconnected | {
"line": 53,
"column": 2
} | {
"line": 53,
"column": 25
} | {
"line": 53,
"column": 26
} | [
{
"pp": "case h\nG : Type u_1\ninst✝³ : TopologicalSpace G\ninst✝² : Group G\ninst✝¹ : NonarchimedeanGroup G\ninst✝ : T2Space G\na b : G\nh : a ≠ b\nu v : Set G\nleft✝ : IsOpen u\nopen_v : IsOpen v\nmem_u : a⁻¹ * b ∈ u\nmem_v : 1 ∈ v\ndis : Disjoint u v\nV : OpenSubgroup G\nhV : ↑V ⊆ v\nx : Set G\nmem_aV : x ⊆ ... | [
"case h\nG : Type u_1\ninst✝³ : TopologicalSpace G\ninst✝² : Group G\ninst✝¹ : NonarchimedeanGroup G\ninst✝ : T2Space G\na b : G\nh : a ≠ b\nu v : Set G\nleft✝ : IsOpen u\nopen_v : IsOpen v\nmem_u : a⁻¹ * b ∈ u\nmem_v : 1 ∈ v\ndis : Disjoint u v\nV : OpenSubgroup G\nhV : ↑V ⊆ v\nx : Set G\nmem_aV : x ⊆ a • ↑V\nmem_... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Topology.Algebra.InfiniteSum.DiscreteConvolution | {
"line": 175,
"column": 2
} | {
"line": 175,
"column": 27
} | {
"line": 175,
"column": 28
} | [
{
"pp": "M : Type u_1\nS : Type u_2\nE : Type u_3\nE' : Type u_4\nF : Type u_6\ninst✝¹⁰ : Monoid M\ninst✝⁹ : CommSemiring S\ninst✝⁸ : AddCommMonoid E\ninst✝⁷ : AddCommMonoid E'\ninst✝⁶ : AddCommMonoid F\ninst✝⁵ : Module S E\ninst✝⁴ : Module S E'\ninst✝³ : Module S F\ninst✝² : TopologicalSpace F\ninst✝¹ : T2Spac... | [
"M : Type u_1\nS : Type u_2\nE : Type u_3\nE' : Type u_4\nF : Type u_6\ninst✝¹⁰ : Monoid M\ninst✝⁹ : CommSemiring S\ninst✝⁸ : AddCommMonoid E\ninst✝⁷ : AddCommMonoid E'\ninst✝⁶ : AddCommMonoid F\ninst✝⁵ : Module S E\ninst✝⁴ : Module S E'\ninst✝³ : Module S F\ninst✝² : TopologicalSpace F\ninst✝¹ : T2Space F\ninst✝ :... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Topology.Algebra.InfiniteSum.DiscreteConvolution | {
"line": 188,
"column": 2
} | {
"line": 188,
"column": 27
} | {
"line": 188,
"column": 28
} | [
{
"pp": "M : Type u_1\nS : Type u_2\nE : Type u_3\nE' : Type u_4\nF : Type u_6\ninst✝¹⁰ : Monoid M\ninst✝⁹ : CommSemiring S\ninst✝⁸ : AddCommMonoid E\ninst✝⁷ : AddCommMonoid E'\ninst✝⁶ : AddCommMonoid F\ninst✝⁵ : Module S E\ninst✝⁴ : Module S E'\ninst✝³ : Module S F\ninst✝² : TopologicalSpace F\ninst✝¹ : T2Spac... | [
"M : Type u_1\nS : Type u_2\nE : Type u_3\nE' : Type u_4\nF : Type u_6\ninst✝¹⁰ : Monoid M\ninst✝⁹ : CommSemiring S\ninst✝⁸ : AddCommMonoid E\ninst✝⁷ : AddCommMonoid E'\ninst✝⁶ : AddCommMonoid F\ninst✝⁵ : Module S E\ninst✝⁴ : Module S E'\ninst✝³ : Module S F\ninst✝² : TopologicalSpace F\ninst✝¹ : T2Space F\ninst✝ :... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Topology.Algebra.InfiniteSum.DiscreteConvolution | {
"line": 203,
"column": 2
} | {
"line": 203,
"column": 27
} | {
"line": 203,
"column": 28
} | [
{
"pp": "M : Type u_1\nS : Type u_2\nE : Type u_3\nE' : Type u_4\ninst✝¹⁰ : Monoid M\ninst✝⁹ : CommSemiring S\ninst✝⁸ : AddCommMonoid E\ninst✝⁷ : AddCommMonoid E'\ninst✝⁶ : Module S E\ninst✝⁵ : Module S E'\nF : Type u_10\ninst✝⁴ : AddCommMonoid F\ninst✝³ : Module S F\ninst✝² : TopologicalSpace F\ninst✝¹ : Conti... | [
"M : Type u_1\nS : Type u_2\nE : Type u_3\nE' : Type u_4\ninst✝¹⁰ : Monoid M\ninst✝⁹ : CommSemiring S\ninst✝⁸ : AddCommMonoid E\ninst✝⁷ : AddCommMonoid E'\ninst✝⁶ : Module S E\ninst✝⁵ : Module S E'\nF : Type u_10\ninst✝⁴ : AddCommMonoid F\ninst✝³ : Module S F\ninst✝² : TopologicalSpace F\ninst✝¹ : ContinuousConstSM... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Topology.Algebra.InfiniteSum.DiscreteConvolution | {
"line": 209,
"column": 2
} | {
"line": 209,
"column": 27
} | {
"line": 209,
"column": 28
} | [
{
"pp": "M : Type u_1\nS : Type u_2\nE : Type u_3\nE' : Type u_4\ninst✝¹⁰ : Monoid M\ninst✝⁹ : CommSemiring S\ninst✝⁸ : AddCommMonoid E\ninst✝⁷ : AddCommMonoid E'\ninst✝⁶ : Module S E\ninst✝⁵ : Module S E'\nF : Type u_10\ninst✝⁴ : AddCommMonoid F\ninst✝³ : Module S F\ninst✝² : TopologicalSpace F\ninst✝¹ : Conti... | [
"M : Type u_1\nS : Type u_2\nE : Type u_3\nE' : Type u_4\ninst✝¹⁰ : Monoid M\ninst✝⁹ : CommSemiring S\ninst✝⁸ : AddCommMonoid E\ninst✝⁷ : AddCommMonoid E'\ninst✝⁶ : Module S E\ninst✝⁵ : Module S E'\nF : Type u_10\ninst✝⁴ : AddCommMonoid F\ninst✝³ : Module S F\ninst✝² : TopologicalSpace F\ninst✝¹ : ContinuousConstSM... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Topology.Algebra.PontryaginDual | {
"line": 56,
"column": 4
} | {
"line": 56,
"column": 20
} | {
"line": 56,
"column": 21
} | [
{
"pp": "case refine_2\nA : Type u_1\nB : Type u_2\nC : Type u_3\nG : Type u_4\nH : Type u_5\ninst✝¹² : Monoid A\ninst✝¹¹ : Monoid B\ninst✝¹⁰ : Monoid C\ninst✝⁹ : CommGroup G\ninst✝⁸ : Group H\ninst✝⁷ : TopologicalSpace A\ninst✝⁶ : TopologicalSpace B\ninst✝⁵ : TopologicalSpace C\ninst✝⁴ : TopologicalSpace G\nin... | [
"case refine_2\nA : Type u_1\nB : Type u_2\nC : Type u_3\nG : Type u_4\nH : Type u_5\ninst✝¹² : Monoid A\ninst✝¹¹ : Monoid B\ninst✝¹⁰ : Monoid C\ninst✝⁹ : CommGroup G\ninst✝⁸ : Group H\ninst✝⁷ : TopologicalSpace A\ninst✝⁶ : TopologicalSpace B\ninst✝⁵ : TopologicalSpace C\ninst✝⁴ : TopologicalSpace G\ninst✝³ : Topol... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Topology.Algebra.PontryaginDual | {
"line": 96,
"column": 6
} | {
"line": 96,
"column": 17
} | {
"line": 96,
"column": 18
} | [
{
"pp": "case refine_1\nA : Type u_1\nB : Type u_2\nC : Type u_3\nG : Type u_4\nH : Type u_5\ninst✝¹² : Monoid A\ninst✝¹¹ : Monoid B\ninst✝¹⁰ : Monoid C\ninst✝⁹ : CommGroup G\ninst✝⁸ : Group H\ninst✝⁷ : TopologicalSpace A\ninst✝⁶ : TopologicalSpace B\ninst✝⁵ : TopologicalSpace C\ninst✝⁴ : TopologicalSpace G\nin... | [
"case refine_1\nA : Type u_1\nB : Type u_2\nC : Type u_3\nG : Type u_4\nH : Type u_5\ninst✝¹² : Monoid A\ninst✝¹¹ : Monoid B\ninst✝¹⁰ : Monoid C\ninst✝⁹ : CommGroup G\ninst✝⁸ : Group H\ninst✝⁷ : TopologicalSpace A\ninst✝⁶ : TopologicalSpace B\ninst✝⁵ : TopologicalSpace C\ninst✝⁴ : TopologicalSpace G\ninst✝³ : Topol... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Topology.Algebra.PontryaginDual | {
"line": 100,
"column": 53
} | {
"line": 100,
"column": 71
} | {
"line": 100,
"column": 72
} | [
{
"pp": "A : Type u_1\nB : Type u_2\nC : Type u_3\nG : Type u_4\nH : Type u_5\ninst✝¹² : Monoid A\ninst✝¹¹ : Monoid B\ninst✝¹⁰ : Monoid C\ninst✝⁹ : CommGroup G\ninst✝⁸ : Group H\ninst✝⁷ : TopologicalSpace A\ninst✝⁶ : TopologicalSpace B\ninst✝⁵ : TopologicalSpace C\ninst✝⁴ : TopologicalSpace G\ninst✝³ : Topologi... | [
"A : Type u_1\nB : Type u_2\nC : Type u_3\nG : Type u_4\nH : Type u_5\ninst✝¹² : Monoid A\ninst✝¹¹ : Monoid B\ninst✝¹⁰ : Monoid C\ninst✝⁹ : CommGroup G\ninst✝⁸ : Group H\ninst✝⁷ : TopologicalSpace A\ninst✝⁶ : TopologicalSpace B\ninst✝⁵ : TopologicalSpace C\ninst✝⁴ : TopologicalSpace G\ninst✝³ : TopologicalSpace H\n... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Topology.Category.TopCat.Sphere | {
"line": 76,
"column": 27
} | {
"line": 76,
"column": 68
} | {
"line": 76,
"column": 69
} | [
{
"pp": "n : ℕ\nx : EuclideanSpace ℝ (Fin n)\nhx : x ∈ Metric.sphere 0 1\ny : EuclideanSpace ℝ (Fin n)\nhy : y ∈ Metric.sphere 0 1\nh :\n (ConcreteCategory.hom (diskBoundaryInclusion n)) { down := ⟨x, hx⟩ } =\n (ConcreteCategory.hom (diskBoundaryInclusion n)) { down := ⟨y, hy⟩ }\n⊢ x = y",
"ppTerm": "?m... | [
"n : ℕ\nx : EuclideanSpace ℝ (Fin n)\nhx : x ∈ Metric.sphere 0 1\ny : EuclideanSpace ℝ (Fin n)\nhy : y ∈ Metric.sphere 0 1\nh :\n (ConcreteCategory.hom (diskBoundaryInclusion n)) { down := ⟨x, hx⟩ } =\n (ConcreteCategory.hom (diskBoundaryInclusion n)) { down := ⟨y, hy⟩ }\n⊢ x = y"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Topology.Category.TopCat.Sphere | {
"line": 82,
"column": 27
} | {
"line": 82,
"column": 60
} | {
"line": 82,
"column": 61
} | [
{
"pp": "n : ℕ\nx : EuclideanSpace ℝ (Fin n)\nhx : x ∈ Metric.ball 0 1\ny : EuclideanSpace ℝ (Fin n)\nhy : y ∈ Metric.ball 0 1\nh :\n (ConcreteCategory.hom (ballInclusion n)) { down := ⟨x, hx⟩ } =\n (ConcreteCategory.hom (ballInclusion n)) { down := ⟨y, hy⟩ }\n⊢ x = y",
"ppTerm": "?m.67",
"assigned"... | [
"n : ℕ\nx : EuclideanSpace ℝ (Fin n)\nhx : x ∈ Metric.ball 0 1\ny : EuclideanSpace ℝ (Fin n)\nhy : y ∈ Metric.ball 0 1\nh :\n (ConcreteCategory.hom (ballInclusion n)) { down := ⟨x, hx⟩ } =\n (ConcreteCategory.hom (ballInclusion n)) { down := ⟨y, hy⟩ }\n⊢ x = y"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Topology.Category.Compactum | {
"line": 146,
"column": 6
} | {
"line": 146,
"column": 11
} | {
"line": 146,
"column": 11
} | [
{
"pp": "X Y : Compactum\nf : X ⟶ Y\nxs : Ultrafilter X.A\n⊢ (ConcreteCategory.hom (X.a ≫ f.f)) xs = Y.str (Ultrafilter.map (⇑(ConcreteCategory.hom f)) xs)",
"ppTerm": "?m.27",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"CategoryTheory.Monad.Algebra.Hom.h",
"CategoryTheory.Cate... | [
"X Y : Compactum\nf : X ⟶ Y\nxs : Ultrafilter X.A\n⊢ (ConcreteCategory.hom (β.map f.f ≫ Y.a)) xs = Y.str (Ultrafilter.map (⇑(ConcreteCategory.hom f)) xs)"
] | ← f.h | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Topology.CWComplex.Classical.Finite | {
"line": 333,
"column": 4
} | {
"line": 333,
"column": 30
} | {
"line": 334,
"column": 2
} | [
{
"pp": "case h\nX : Type u_2\ninst✝¹ : TopologicalSpace X\nC D : Set X\ninst✝ : RelCWComplex C D\nfinite : _root_.Finite ((n : ℕ) × cell C n)\nh✝ : Nonempty ((n : ℕ) × cell C n)\nx✝ : Fintype ((n : ℕ) × cell C n)\nA : Finset ℕ := Finset.image Sigma.fst Finset.univ\nm : ℕ\na✝ : A.max' ⋯ + 1 ≤ m\nh' : Nonempty (... | [] | linarith [A.le_max' m hmA] | Mathlib.Tactic._aux_Mathlib_Tactic_Linarith_Frontend___elabRules_Mathlib_Tactic_linarith_1 | Mathlib.Tactic.linarith |
Mathlib.Topology.Convenient.ContinuousMapGeneratedBy | {
"line": 72,
"column": 2
} | {
"line": 72,
"column": 41
} | {
"line": 72,
"column": 42
} | [
{
"pp": "ι : Type t\nX : ι → Type u\ninst✝¹ : (i : ι) → TopologicalSpace (X i)\nY : Type v\ninst✝ : TopologicalSpace Y\n⊢ ContinuousGeneratedBy X _root_.id",
"ppTerm": "?m.9",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Continuous",
"Equiv.instEquivLike",
"Equiv.symm_comp... | [
"ι : Type t\nX : ι → Type u\ninst✝¹ : (i : ι) → TopologicalSpace (X i)\nY : Type v\ninst✝ : TopologicalSpace Y\n⊢ Continuous _root_.id"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Topology.Category.Compactum | {
"line": 251,
"column": 6
} | {
"line": 251,
"column": 16
} | {
"line": 252,
"column": 6
} | [
{
"pp": "X : Compactum\nA : Set X.A\nF : Ultrafilter X.A\nhF : F ∈ basic (cl A)\nfsu : Type u_1 := Finset (Set (Ultrafilter X.A))\nssu : Type u_1 := Set (Set (Ultrafilter X.A))\nι : fsu → ssu := fun x ↦ ↑x\nC0 : ssu := {Z | ∃ B ∈ F, X.str ⁻¹' B = Z}\nAA : Set (Ultrafilter X.A) := {G | A ∈ G}\nC1 : ssu := insert... | [
"X : Compactum\nA : Set X.A\nF : Ultrafilter X.A\nhF : F ∈ basic (cl A)\nfsu : Type u_1 := Finset (Set (Ultrafilter X.A))\nssu : Type u_1 := Set (Set (Ultrafilter X.A))\nι : fsu → ssu := fun x ↦ ↑x\nC0 : ssu := {Z | ∃ B ∈ F, X.str ⁻¹' B = Z}\nAA : Set (Ultrafilter X.A) := {G | A ∈ G}\nC1 : ssu := insert AA C0\nC2 :... | intro P hP | Lean.Elab.Tactic.evalIntro | Lean.Parser.Tactic.intro |
Mathlib.Topology.Category.Compactum | {
"line": 256,
"column": 4
} | {
"line": 256,
"column": 14
} | {
"line": 257,
"column": 4
} | [
{
"pp": "X : Compactum\nA : Set X.A\nF : Ultrafilter X.A\nhF : F ∈ basic (cl A)\nfsu : Type u_1 := Finset (Set (Ultrafilter X.A))\nssu : Type u_1 := Set (Set (Ultrafilter X.A))\nι : fsu → ssu := fun x ↦ ↑x\nC0 : ssu := {Z | ∃ B ∈ F, X.str ⁻¹' B = Z}\nAA : Set (Ultrafilter X.A) := {G | A ∈ G}\nC1 : ssu := insert... | [
"X : Compactum\nA : Set X.A\nF : Ultrafilter X.A\nhF : F ∈ basic (cl A)\nfsu : Type u_1 := Finset (Set (Ultrafilter X.A))\nssu : Type u_1 := Set (Set (Ultrafilter X.A))\nι : fsu → ssu := fun x ↦ ↑x\nC0 : ssu := {Z | ∃ B ∈ F, X.str ⁻¹' B = Z}\nAA : Set (Ultrafilter X.A) := {G | A ∈ G}\nC1 : ssu := insert AA C0\nC2 :... | intro P hP | Lean.Elab.Tactic.evalIntro | Lean.Parser.Tactic.intro |
Mathlib.Topology.CWComplex.Classical.Basic | {
"line": 175,
"column": 15
} | {
"line": 175,
"column": 45
} | {
"line": 175,
"column": 46
} | [
{
"pp": "X : Type u_1\ninst✝¹ : TopologicalSpace X\nC : Set X\ninst✝ : CWComplex C\n⊢ ∀ (n : ℕ) (i : CWComplex.cell C n),\n ∃ I,\n MapsTo (↑(CWComplex.map n i)) (sphere 0 1)\n (∅ ∪ ⋃ m, ⋃ (_ : m < n), ⋃ j ∈ I m, ↑(CWComplex.map m j) '' closedBall 0 1)",
"ppTerm": "?m.41",
"assigned": true... | [
"X : Type u_1\ninst✝¹ : TopologicalSpace X\nC : Set X\ninst✝ : CWComplex C\n⊢ ∀ (n : ℕ) (i : CWComplex.cell C n),\n ∃ I,\n MapsTo (↑(CWComplex.map n i)) (sphere 0 1) (⋃ m, ⋃ (_ : m < n), ⋃ j ∈ I m, ↑(CWComplex.map m j) '' closedBall 0 1)"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Topology.CWComplex.Classical.Basic | {
"line": 176,
"column": 16
} | {
"line": 176,
"column": 72
} | {
"line": 176,
"column": 73
} | [
{
"pp": "X : Type u_1\ninst✝¹ : TopologicalSpace X\nC : Set X\ninst✝ : CWComplex C\n⊢ ∀ A ⊆ C,\n (∀ (n : ℕ) (j : CWComplex.cell C n), IsClosed[inst✝¹] (A ∩ ↑(CWComplex.map n j) '' closedBall 0 1)) ∧\n IsClosed[inst✝¹] (A ∩ ∅) →\n IsClosed[inst✝¹] A",
"ppTerm": "?m.52",
"assigned": true,
... | [
"X : Type u_1\ninst✝¹ : TopologicalSpace X\nC : Set X\ninst✝ : CWComplex C\n⊢ ∀ A ⊆ C,\n (∀ (n : ℕ) (j : CWComplex.cell C n), IsClosed[inst✝¹] (A ∩ ↑(CWComplex.map n j) '' closedBall 0 1)) →\n IsClosed[inst✝¹] A"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Topology.CWComplex.Classical.Basic | {
"line": 178,
"column": 15
} | {
"line": 178,
"column": 45
} | {
"line": 178,
"column": 46
} | [
{
"pp": "X : Type u_1\ninst✝¹ : TopologicalSpace X\nC : Set X\ninst✝ : CWComplex C\n⊢ ∅ ∪ ⋃ n, ⋃ j, ↑(CWComplex.map n j) '' closedBall 0 1 = C",
"ppTerm": "?m.63",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Real",
"pseudoMetricSpacePi",
"outParam",
"Real.instZero",... | [
"X : Type u_1\ninst✝¹ : TopologicalSpace X\nC : Set X\ninst✝ : CWComplex C\n⊢ ⋃ n, ⋃ j, ↑(CWComplex.map n j) '' closedBall 0 1 = C"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Topology.CWComplex.Classical.Basic | {
"line": 190,
"column": 16
} | {
"line": 190,
"column": 27
} | {
"line": 190,
"column": 28
} | [
{
"pp": "X : Type u_1\ninst✝¹ : TopologicalSpace X\nC : Set X\ninst✝ : RelCWComplex C ∅\n⊢ ∀ (n : ℕ) (i : cell C n),\n ∃ I, MapsTo (↑(map n i)) (sphere 0 1) (⋃ m, ⋃ (_ : m < n), ⋃ j ∈ I m, ↑(map m j) '' closedBall 0 1)",
"ppTerm": "?m.42",
"assigned": false,
"usedConstants": [],
"usedFVars": ... | [
"X : Type u_1\ninst✝¹ : TopologicalSpace X\nC : Set X\ninst✝ : RelCWComplex C ∅\n⊢ ∀ (n : ℕ) (i : cell C n),\n ∃ I, MapsTo (↑(map n i)) (sphere 0 1) (⋃ m, ⋃ (_ : m < n), ⋃ j ∈ I m, ↑(map m j) '' closedBall 0 1)"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Topology.CWComplex.Classical.Basic | {
"line": 191,
"column": 16
} | {
"line": 191,
"column": 27
} | {
"line": 191,
"column": 28
} | [
{
"pp": "X : Type u_1\ninst✝¹ : TopologicalSpace X\nC : Set X\ninst✝ : RelCWComplex C ∅\n⊢ ∀ A ⊆ C, (∀ (n : ℕ) (j : cell C n), IsClosed[inst✝¹] (A ∩ ↑(map n j) '' closedBall 0 1)) → IsClosed[inst✝¹] A",
"ppTerm": "?m.56",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": ... | [
"X : Type u_1\ninst✝¹ : TopologicalSpace X\nC : Set X\ninst✝ : RelCWComplex C ∅\n⊢ ∀ A ⊆ C, (∀ (n : ℕ) (j : cell C n), IsClosed[inst✝¹] (A ∩ ↑(map n j) '' closedBall 0 1)) → IsClosed[inst✝¹] A"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Topology.CWComplex.Classical.Basic | {
"line": 192,
"column": 15
} | {
"line": 192,
"column": 26
} | {
"line": 192,
"column": 27
} | [
{
"pp": "X : Type u_1\ninst✝¹ : TopologicalSpace X\nC : Set X\ninst✝ : RelCWComplex C ∅\n⊢ ⋃ n, ⋃ j, ↑(map n j) '' closedBall 0 1 = C",
"ppTerm": "?m.70",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"X : Type u_1\ninst✝¹ : TopologicalSpace X\nC : Set X\ninst✝ : RelCWComplex C ∅\n⊢ ⋃ n, ⋃ j, ↑(map n j) '' closedBall 0 1 = C"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Topology.Category.Profinite.Nobeling.Basic | {
"line": 114,
"column": 2
} | {
"line": 114,
"column": 28
} | {
"line": 114,
"column": 29
} | [
{
"pp": "I : Type u\nJ : I → Prop\ninst✝ : (i : I) → Decidable (J i)\nx : I → Bool\nh : ∀ (i : I), x i ≠ false → J i\ni : I\n⊢ false ≠ x i → J i",
"ppTerm": "?m.19",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"I : Type u\nJ : I → Prop\ninst✝ : (i : I) → Decidable (J i)\nx : I → Bool\nh : ∀ (i : I), x i ≠ false → J i\ni : I\n⊢ false ≠ x i → J i"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Topology.Category.Compactum | {
"line": 370,
"column": 6
} | {
"line": 370,
"column": 32
} | {
"line": 370,
"column": 32
} | [
{
"pp": "X Y : Compactum\nf : X ⟶ Y\n⊢ Continuous ⇑(ConcreteCategory.hom f)",
"ppTerm": "?m.8",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Continuous",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"congrArg",
"CategoryTheory.ConcreteCategory.hom",
... | [
"X Y : Compactum\nf : X ⟶ Y\n⊢ ∀ (x : X.A) (g : Ultrafilter X.A),\n ↑g ≤ 𝓝 x → Tendsto (⇑(ConcreteCategory.hom f)) (↑g) (𝓝 ((ConcreteCategory.hom f) x))"
] | continuous_iff_ultrafilter | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Topology.Category.Profinite.Nobeling.Span | {
"line": 159,
"column": 2
} | {
"line": 159,
"column": 64
} | {
"line": 160,
"column": 2
} | [
{
"pp": "I : Type u\nC : Set (I → Bool)\ninst✝ : LinearOrder I\ns : Finset I\na : I\nas : List I\nha : List.IsChain (fun x1 x2 ↦ x1 > x2) (a :: as)\nc : Products I →₀ ℤ\nhc : ↑c.support ⊆ {m | ↑m ≤ as}\nm : Products I\nhm : c m ≠ 0\n⊢ e (π C fun x ↦ x ∈ s) a * c m • Products.eval (π C fun x ↦ x ∈ s) m ∈\n Su... | [
"I : Type u\nC : Set (I → Bool)\ninst✝ : LinearOrder I\ns : Finset I\na : I\nas : List I\nha : List.IsChain (fun x1 x2 ↦ x1 > x2) (a :: as)\nc : Products I →₀ ℤ\nhc : ↑c.support ⊆ {m | ↑m ≤ as}\nm : Products I\nhm : c m ≠ 0\nhsm :\n ∀ (c : ℤ) (x : LocallyConstant ↑(π C fun x ↦ x ∈ s) ℤ),\n (LinearMap.mulLeft ℤ ... | have hsm := (LinearMap.mulLeft ℤ (e (π C (· ∈ s)) a)).map_smul | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_tacticHave___1 | Lean.Parser.Tactic.tacticHave__ |
Mathlib.Topology.Category.Profinite.Nobeling.Span | {
"line": 166,
"column": 4
} | {
"line": 166,
"column": 62
} | {
"line": 166,
"column": 63
} | [
{
"pp": "I : Type u\nC : Set (I → Bool)\ninst✝ : LinearOrder I\ns : Finset I\na : I\nas : List I\nha : List.IsChain (fun x1 x2 ↦ x1 > x2) (a :: as)\nc : Products I →₀ ℤ\nhc : ↑c.support ⊆ {m | ↑m ≤ as}\nm : Products I\nhm : c m ≠ 0\nhsm :\n ∀ (c : ℤ) (x : LocallyConstant ↑(π C fun x ↦ x ∈ s) ℤ),\n e (π C fu... | [
"I : Type u\nC : Set (I → Bool)\ninst✝ : LinearOrder I\ns : Finset I\na : I\nas : List I\nha : List.IsChain (fun x1 x2 ↦ x1 > x2) (a :: as)\nc : Products I →₀ ℤ\nhc : ↑c.support ⊆ {m | ↑m ≤ as}\nm : Products I\nhm : c m ≠ 0\nhsm :\n ∀ (c : ℤ) (x : LocallyConstant ↑(π C fun x ↦ x ∈ s) ℤ),\n e (π C fun x ↦ x ∈ s)... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Topology.Category.Compactum | {
"line": 400,
"column": 8
} | {
"line": 400,
"column": 18
} | {
"line": 401,
"column": 8
} | [
{
"pp": "X : Type u_1\ninst✝² : TopologicalSpace X\ninst✝¹ : CompactSpace X\ninst✝ : T2Space X\nFF : Ultrafilter (Ultrafilter X)\nx : X := ⋯\nc1 : x = (Ultrafilter.map Ultrafilter.lim FF).lim\nc2 : ∀ (U : Set X) (F : Ultrafilter X), F.lim ∈ U → IsOpen[inst✝²] U → U ∈ F\nc3 : ↑(Ultrafilter.map Ultrafilter.lim FF... | [
"X : Type u_1\ninst✝² : TopologicalSpace X\ninst✝¹ : CompactSpace X\ninst✝ : T2Space X\nFF : Ultrafilter (Ultrafilter X)\nx : X := (Ultrafilter.map Ultrafilter.lim FF).lim\nc1 : x = (Ultrafilter.map Ultrafilter.lim FF).lim\nc2 : ∀ (U : Set X) (F : Ultrafilter X), F.lim ∈ U → IsOpen[inst✝²] U → U ∈ F\nc3 : ↑(Ultrafi... | intro P hP | Lean.Elab.Tactic.evalIntro | Lean.Parser.Tactic.intro |
Mathlib.Topology.Category.Compactum | {
"line": 411,
"column": 10
} | {
"line": 411,
"column": 36
} | {
"line": 411,
"column": 36
} | [
{
"pp": "X Y : Compactum\nf : X.A → Y.A\ncont : Continuous f\n⊢ failed to pretty print expression (use 'set_option pp.rawOnError true' for raw representation)",
"ppTerm": "?m.17",
"assigned": true,
"usedConstants": [
"Continuous",
"congrArg",
"PartialOrder.toPreorder",
"Categ... | [
"X Y : Compactum\nf : X.A → Y.A\ncont : ∀ (x : X.A) (g : Ultrafilter X.A), ↑g ≤ 𝓝 x → Tendsto f (↑g) (𝓝 (f x))\n⊢ failed to pretty print expression (use 'set_option pp.rawOnError true' for raw representation)"
] | continuous_iff_ultrafilter | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Topology.CWComplex.Classical.Basic | {
"line": 516,
"column": 4
} | {
"line": 516,
"column": 23
} | {
"line": 516,
"column": 24
} | [
{
"pp": "X : Type u_1\nt : TopologicalSpace X\nC D : Set X\ninst✝ : RelCWComplex C D\nthis : D ∪ ⋃ n, ⋃ j, openCell n j = D ∪ ⋃ m, ⋃ (_ : ↑m < ⊤), ⋃ j, closedCell m j\n⊢ D ∪ ⋃ n, ⋃ j, openCell n j = C",
"ppTerm": "?m.59",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": ... | [
"X : Type u_1\nt : TopologicalSpace X\nC D : Set X\ninst✝ : RelCWComplex C D\nthis : D ∪ ⋃ n, ⋃ j, openCell n j = D ∪ ⋃ m, ⋃ (_ : ↑m < ⊤), ⋃ j, closedCell m j\n⊢ D ∪ ⋃ n, ⋃ j, openCell n j = C"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Topology.CWComplex.Classical.Basic | {
"line": 521,
"column": 2
} | {
"line": 521,
"column": 13
} | {
"line": 521,
"column": 14
} | [
{
"pp": "X : Type u_1\nt : TopologicalSpace X\nC : Set X\ninst✝ : CWComplex C\n⊢ ⋃ n, ⋃ j, openCell n j = C",
"ppTerm": "?m.19",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"X : Type u_1\nt : TopologicalSpace X\nC : Set X\ninst✝ : CWComplex C\n⊢ ⋃ n, ⋃ j, openCell n j = C"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Topology.Category.Profinite.Nobeling.Basic | {
"line": 426,
"column": 2
} | {
"line": 426,
"column": 24
} | {
"line": 426,
"column": 25
} | [
{
"pp": "I : Type u\nC : Set (I → Bool)\ninst✝¹ : LinearOrder I\nl : Products I\nJ : I → Prop\ninst✝ : (j : I) → Decidable (J j)\nh✝ : isGood (π C J) l\ni : I\nhi : i ∈ ↑l\nh' : ¬J i\nw✝ : I → Bool\nleft✝ : w✝ ∈ C\nh : ∀ i ∈ ↑l, ↑⟨Proj J w✝, ⋯⟩ i = true\n⊢ False",
"ppTerm": "?m.85",
"assigned": false,
... | [
"I : Type u\nC : Set (I → Bool)\ninst✝¹ : LinearOrder I\nl : Products I\nJ : I → Prop\ninst✝ : (j : I) → Decidable (J j)\nh✝ : isGood (π C J) l\ni : I\nhi : i ∈ ↑l\nh' : ¬J i\nw✝ : I → Bool\nleft✝ : w✝ ∈ C\nh : ∀ i ∈ ↑l, ↑⟨Proj J w✝, ⋯⟩ i = true\n⊢ False"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Topology.Category.Profinite.Nobeling.Span | {
"line": 216,
"column": 17
} | {
"line": 216,
"column": 75
} | {
"line": 216,
"column": 76
} | [
{
"pp": "I : Type u\nC : Set (I → Bool)\ninst✝¹ : LinearOrder I\ns : Finset I\ninst✝ : WellFoundedLT I\nx : ↑(π C fun x ↦ x ∈ s)\nl : List I := s.sort fun x1 x2 ↦ x1 ≥ x2\na : I\nas : List I\nha : List.IsChain (fun x1 x2 ↦ x1 > x2) (a :: as)\nc : Products I →₀ ℤ\nhc : ↑c.support ⊆ {m | ↑m ≤ as}\nhmap :\n ∀ (g ... | [
"I : Type u\nC : Set (I → Bool)\ninst✝¹ : LinearOrder I\ns : Finset I\ninst✝ : WellFoundedLT I\nx : ↑(π C fun x ↦ x ∈ s)\nl : List I := s.sort fun x1 x2 ↦ x1 ≥ x2\na : I\nas : List I\nha : List.IsChain (fun x1 x2 ↦ x1 > x2) (a :: as)\nc : Products I →₀ ℤ\nhc : ↑c.support ⊆ {m | ↑m ≤ as}\nhmap :\n ∀ (g : Products I... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Topology.Category.Profinite.Nobeling.Successor | {
"line": 158,
"column": 4
} | {
"line": 158,
"column": 26
} | {
"line": 158,
"column": 27
} | [
{
"pp": "case pos\nI : Type u\nC : Set (I → Bool)\ninst✝¹ : LinearOrder I\ninst✝ : WellFoundedLT I\no : Ordinal.{u}\nhsC : contained C (Order.succ o)\nho : o < Ordinal.type fun x1 x2 ↦ x1 < x2\ng : I → Bool\nhg : g ∈ C1 C ho\ni : I\nh : term I ho = i\n⊢ true = g i",
"ppTerm": "?pos✝",
"assigned": true,
... | [
"case pos\nI : Type u\nC : Set (I → Bool)\ninst✝¹ : LinearOrder I\ninst✝ : WellFoundedLT I\no : Ordinal.{u}\nhsC : contained C (Order.succ o)\nho : o < Ordinal.type fun x1 x2 ↦ x1 < x2\ng : I → Bool\nhg : g ∈ C1 C ho\ni : I\nh : term I ho = i\n⊢ true = g (term I ho)"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
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